{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<small><i>This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com). Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_tutorial/).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supervised Learning In-Depth: Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we introduced supervised machine learning.\n",
    "There are many supervised learning algorithms available; here we'll go into brief detail one of the most powerful and interesting methods: **Support Vector Machines (SVMs)**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jakevdp/anaconda/envs/python3.5/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
      "  warnings.warn(self.msg_depr % (key, alt_key))\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "# use seaborn plotting defaults\n",
    "import seaborn as sns; sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Support Vector Machines (SVMs) are a powerful supervised learning algorithm used for **classification** or for **regression**. SVMs are a **discriminative** classifier: that is, they draw a boundary between clusters of data.\n",
    "\n",
    "Let's show a quick example of support vector classification. First we need to create a dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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L6PV63H7rF0y+OKlirH1pe7Td1BZLP1qJ+Pdsc/Th6MrDuL8oF26XXVHqXQrdQAMGvzkU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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10abd3d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y = make_blobs(n_samples=50, centers=2,\n",
    "                  random_state=0, cluster_std=0.60)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A discriminative classifier attempts to draw a line between the two sets of data. Immediately we see a problem: such a line is ill-posed! For example, we could come up with several possibilities which perfectly discriminate between the classes in this example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z8zN3eG2SJGbRqrr06krn3V0481Mq8RdO039cKM90GWTusIQwm/AZUZz401HS\nPjrDkMxI7jjcITXqDH3+HIKTk1PDF2gBOp2Offu+IiZmNfHxPwEQHNyfFStWMW/eczg6OpolLktX\nXl5OSkoyCQnxJCbG8/XXe5t0HUnMotWpVCpChw0CWTosBAAjXx1L9eJqMlMzcPVwZVqv2WaJo6Sk\nmE8+2cy6dTFcu3YVgMmTp6LRrGL06LGykqEWRVG4fPkSCQlxJCbGk5AQT3p6Gnq9/qmvLYlZCCEs\ngJ2dHaERA83y3pcvX2Lduhi2bt1CaeldnJycePnlZURHv0Hv3n3MEpOlKS0t5fTppHtJuCYZ5+fn\nG9vt7e0JC4sgMnIIkZFRREbW3fq3sSQxCyFEO6QoCj/9dIrY2NXs2/cVBoOBDh068vOf/5IlS17B\n29vH3CGajaIoZGdfID4+jsTEBBIS4sjISMdgMBjP6dKlK3PnzicycggREVEMGDCw2dacS2IWQoh2\npLq6mr179xAbu5rTp5MBGDQoDI1mJbNnz8Pe3t7MEba+u3dLSEpKNOkNFxUVGdsdHR2JihpKRESU\nsUfckhunSGIWQoh2oKiokM2bP2b9+rXcunUTlUrF9OmzeOONNxk6dHi7eX5sMBi4cCHLmIQTEuLI\nzMxAURTjOYGB3Rg/fqKxN9y/f2irfmCRxCyEEG3YxYtZrF37AZ9+upXy8nJcXFx5/fUVLF++gqCg\nHuYOr8UVF98hKSnR2BNOTEyguPiOsd3Z2Znhw0cae8Ph4ZFmLyIiiVlYrNLSUuK/OoW9iwNDpw9v\n98XThWgsRVE4fvwHYmNX8+23+4GaZ6K/+tXvWbRoCR4enmaOsGUYDAbOncs0GZI+f/6cSW84KKgH\nkydPJTJyCFFRQwgO7m9xf1ssKxoh7jmy+jtcNtgz59oMKqjg2+CDeP7Kl7CZkeYOTQiLVVlZyccf\n7+Jvf3uP9PQ0ACIjh7BixSpmzHjG4hLQ0yoqKiQpKYH4+DgSEuJJTk7k7t0SY7uLiyujRo251xuO\nIjw8Cl9fXzNG3Dht67sk2oSk/fEM/usA+lT0BsABB57PWMCB335LTlgOAZ2su1atEM0tPz+fjRvX\ns2HDh+Tl5WJjY8OcOfPRaFY+1bIdS6LX68nMzKi1bjiOCxeyTM7p2bMXM2bMMj4bDg4Oscraz5KY\nhcUp3JPP1IoJdY5PuT2ZTz76lKm/n2mGqISwPJmZGaxdu4adOz9Fq9Xi7u7B22+/zcKFr9KlS1dz\nh/dUCgq9YEn3AAAgAElEQVQKSEx8sHlHUlIiZWWlxnZXVzfGjBl/b81wFOHhkW1miVerJeZRo0bh\n4eGNn58/vr6++Pn53/vPDz8/P3x9/XB392g3MwPFo9kW1v8JV4UKu0L5LCnaN0VROHLkELGxqzly\n5BAA3bp1Jzr6DV56aTFBQZ3Iy7tr5iifjE6nIyMj/d664XiSkxO4cOGCyTl9+vS9t1Sppjfcp09f\nq+wNN0ar/ZU7efKkyeLs+jg4OODrW5OkaxK2fz1f1yR0b2/vNvtNae8qA6vqPa5FC73kg5tonyoq\nKti581PWrl3DuXOZAAwfPhKNZhVTp063qr+Hubm592ZI1wxJnz6dRHl5ubHd09PTZLlSRERkm52w\nVp8mJ2aDwcAf/vAHLl26hFqt5l/+5V/o1avXI8+vrq7m3Lkr5OXlkp+fR15e7r2v82t9nUdeXh6Z\nmWdJSal87Pur1Wq8vX0eSt4PEnftXrmvr1+z7cgiWl6fZSEcOnSIiTcnmhz/bMBOxr0yxUxRCWEe\nOTk5fPTRh2zcuJ6CggJsbW157rkXWLFiFQMHDjZ3eA2qrq4mPT3t3prhmmHpq1cvG9tVKhX9+oUY\nt7GMiIhi+PBwCgrKzBe0mTU5MR8+fBiVSsW2bduIi4vjvffeY82aNY88X61W4+vr26gZcYqiUFp6\nl7y8mkRtmsjz7h2v+frGjetkZKQ3eE13dw/jkPn9IfT7X9c+5ufnh6urmwypm1FQSA8yVmv55B/b\n8Ur1QGdXzZ2ouwz+fZTZqu0I0drS0lKJjV3Nnj07qa6uxsvLi1/84m1ee+31Ft116mnl5Ny+N0u6\nZlg6JSUZrVZrbPfy8mLSpCnGJBweHoGbm7vJNdRqy6lDbQ5NTsyTJk1iwoSaCTo3btzAw8Oj2YJS\nqVS4ubnj5uZOjx49Gzxfq9VSUJBfby/84eR+6VJ2g0Pqjo6OJr3u+4k7KKgrjo5uJse8vb3b/Q9R\nSwgeGULwyBC0Wi02NjbY2dmZOyQhWpzBYODgwQPExq7m+PEfAOjVqzfR0St5/vmXcHZ2NnOEpqqq\nqkhLS6m1i1Y8169fM7ar1WqCg/vfS8KRREUNoUePXtLxaYBKqb3yugl+85vf8N133/E///M/jBgx\norniajF6vZ78/Hxyc3PJzc0lJyeHnJwc49e1j+Xk5FBVVf/zzvvUajV+fn4EBATg7+9PQEDAI7/2\n85MhdSFEXaWlpWzcuJH//u//JiurZgnQpEmTeOutt5g2bZrFfPi/fv06p06d4uTJk5w6dYrExEQq\nKx88dvT19WX48OEMGzaM4cOHExkZiZubmxkjtk5PnZihZlr7ggUL+Oabbx5bQNvaZgoqisLduyXk\n5+eRm5tHVdVdLl68Wu+Qel5ensnC9kfx8PB8aBjd9Fl47SF1FxfXFvlk6efnZnXfi/q0hftoC/cA\nbeM+zHEPN25cZ/36tWze/DHFxXdwcHDg2WefJzp6JSEh/Zt0zea6D61WS2pqiskuWjdv3jC229jY\n0L9/KJGRUcbtLLt3D2qWv1lt4ecJau6jKZo8lP3FF1+Qk5NDdHQ0Dg4OqNVqi/lU11xUKhXu7h64\nu3vQo0evBn9YKioqyM+v/Uzc9Nl47SH2ixcv0NBnIicnpzrPw02/fjDxzdPTq839+wvRViUlJRAb\nu5q9ez9Hr9fj6+vHO+/8lldeWY6fn1+rx6MoCtevXzPZvCMtLZXq6mrjOX5+/kyfPouIiCiiooYw\naFCYxQ2ttxVNTsxTpkzht7/9LYsXL0an0/H73/++XZYLq83JyYmuXQPp2jWwwXN1Oh0FBQUms9Tr\nm6Gen59HamqKyS9IfWxtbfHx8a332fjDM9Y9PR89qiGEaBk6nY59+74iJmY18fE/ARAcHIJGs4r5\n8xc8drSxuZWXl5Oaetq4bjghIY7c3Bxju62tLaGhA4094YiIKAIDu8mz4VbS5MTs5OTE3//+9+aM\npV2xtbU1PoNuiKIoFBffMSbqmqF104lutSe3nTmT2uA1vby8Hup5103m9792cXFpjlsWol26e7eE\nTz7ZxLp1sVy9egWASZOmoNGsYsyYcS2e7BRF4cqVy7V6w/Gkp6eh0+mM5wQEdGDmzNnGJDxo0GBZ\nAWFGso2SFVCpVHh6euHp6UXv3n0aPL+8vLxOL7z2krM7dwq5des2+fl5ZGWdb/B6zs4u9awVr3+5\nmaenl3yqFgK4cuUy69bF8MknmyktvYuTkxNLl76GRrOyUb/HTVVWVsaJE8dMZkrn5+cZ2+3t7Rk0\nKMxk3XDnzl3k99aCSGJug5ydnQkM7EZgYLd622s/K68ZUs9/6Hn4w8n8/pD66UYNqde/e1vdrVh9\nfHxlGZRoUxRFIS7uJ2JjV/PNN19iMBgICOjAz372FkuXvtrsezkrisKlS9n3EnAciYkJnD17Br1e\nbzync+cuzJ49zzhJKzR0UKsOm4snJ4m5nasZUu9AQECHBs+tPaT+cC88L8907Xh29sVGDal7e3s/\n1POuO7Ht/v/L0JqwVNXV1Xz55efExq4mOTkJgNDQQWg0K5k799lmm39TWnqX5OQk47B0YmI8BQUF\nxnYHBweGDRvGwIHh9/aVjqJjx07N8t6i9UhiFo32pEPqZWVlj+yFm24Ck8v58+cavJ6Li6tJLzww\nsDMuLh74+fnj72/aM/fw8JShOdHi7twpYtOmj9mwYS03b95ApVIxbdpMVqxYxfDhI5/qZ9BgMHDx\n4gUSE+ONk7QyM8+abJAUGNiNMWPGGYekBwwYSOfOPm1iqVF7JolZtBgXFxdcXILo3j2owXOrqqoo\nLCyos2NbfUPqSUkJJkN19bG3tzcZUq9votv9BO/j49PmCsiLlpWdfYG1az9g+/ZPKC8vx9nZheXL\nNSxfvqJRuxXWp6SkmKSkRJPe8J07d4ztTk5ODBkyzJiEIyOjGjXSJayP/DUSFsHe3p4OHTo2ag9g\ng8HAnTtF6PXlnD9/+ZH7qOfl5ZGVdY7U1NOPvZ5KpcLb27tRM9T9/Pzl+Vw7pSgKJ04cIzZ2Nd9+\nux9FUejcuQvvvPM7Fi9e+kTVjwwGA1lZ52tN0Irj3LlMk70NuncPYuLEKcbtLPv3D5U5Ge2EJGZh\ndR5UFuuOn1/DxeBLS0sfkbhNh9hv375FZmZGg9dzdXV7TC/cNJlLjXHrV1VVxZ49O4mNXWOcNxER\nEYlGs4pZs+Y0arTlzp0ikpIS7lVXiiMpKZGSkmJju7OzCyNGjKpV5jDKLBuNCMsgiVm0ea6urri6\nuhIU1KPBc6uqqowFUR6sF3+4wllN+9WrVxo9pF47adee1NarVzfs7FylxrgFKigoYOPG9WzY8CG5\nuTmo1Wpmz56HRrOSqKihj3ydXq/n3LlMk120Hl6W2LNnL6ZNm2FMxMHBIfI4RRjJT4IQtdjb29Ox\nY6dGzWQ1GAwUFRU9NJReN5E/XY3x2gldaoy3hvPnzxEbu4YdO7ah1Wpxc3PnjTf+ieXLNfXu6ldQ\nUEBS0v0h6QSSkxMpLX0w+crV1Y3Ro8cRFVWzbjg8PLLZl02JtkUSsxBNpFar8fHxwcfHh379gh97\n7sM1xu8n8vLyYq5cud4sNcbrL4hSc0xqjD+eoih8++23/Md//CeHD38HQLdu3YmOfoOXXlqMq2tN\nMQKdTkdGxtla64bjyc6+aHKt3r37EBk5x9gb7tu3n4yEiCciiVmIVvCoGuOPKoxSu8Z47WfjDxL4\ng+Vmja0x3pgZ6n5+/nh5ebWbRFJRUcGuXZ+xdu0a4/yCYcNGoNGsYtq0GRQWFnL8+INdtJKTkygv\nLzO+3t3dg3HjJhgLO4SHR+Lp6WWu2xFthCRmISyQo6MjnTt3oXPnLg2eq9frKSwsfOg5eF69z8bP\nnk03qZ9bn5qRAF+TIfX7SbtmvfiDNmsdUs/JyeGjjz5k48b1FBQUYGtry0svvcSoUeMpKSnhq6++\n4M9//j1Xrlw2vkalUtG3bz+Twg59+vSVqm6i2TVLPebGsvZF722pRqjch2Vo7Xt4uMb445N542uM\nBwT44+39qOpmNcf8/f1brMZ4Y505k0Zs7Gr27NlJVVUVzs7OBAf3R1EUMjLSqaioMJ7r6elpnCFd\n82w4And3D7PF3ljye2E5Wr0esxDC+jxcY7whWq223hnp9e3olpWV1ega43WH0OsviNIcvVGDwcC+\nfV/z97//JykpNWva78+ALi8vJzExHrVazYABAxg0KIKoqJrecM+evaQ3LMxCErMQ4pEcHR3p0qUr\nXbo8fr24n58bt24VUVBQUGdG+v1SpbX/Py0ttdE1xh9VEMXf399kSL325hu3bt3k+PFjbN++hbi4\nn6is1Jpc293d3dgTjowcQlhYOEFBndpEL01YP0nMQohm8aQ1xktKik1mo+fm1r8JzOXLl0hPT2vw\nmk5OTtjY2FBZWVkn6bu4uBAWFsGkSVMYO3Y8ISEDZJa6sFiSmIUQrU6lUuHh4YmHhye9evVu8PwH\nNcZr1oQnJSWQmZnBlSuXyM/Px2AwmDwfflhZWRnHj//A8eM/ADWlUX19768Rr+mF1y6KUrtn7uXl\nLUlctCpJzEIIi1VRUUFqaorJuuHbt28Z221tbQkM7EZFRQU5ObcB6NOnLwsXLmXYsOEUFxc/divW\nptQYf9RyM6kxLpqLJGYhhEVQFIWrV68Y1wwnJsaTlpaKTqcznhMQ0IGZM2czYEAoBQX57N+/j8uX\nLwEwYcIkNJpVjBs3odE93No1xnW6MrKyLtd6Pp5P7Rnrja0x7uXl1eDEtvtfOzs7N+0fS7RpkpiF\nEGZRVlZGaupp4uMf9Ibz8nKN7XZ2dgwaNNhk3bDBYGDduljWrPlf7t4twdHRkSVLXkWjWUmfPn2f\nOIbaNcb9/NwIDg5rMOZHbb36cM3xJ6kx/mDovO5WrFJjvP2RxCyEaHGKonD58qVaQ9IJpKenmRQB\n6dixE888M9eYhAcOHISjoyOKohAfH8ef//wHvv56LwaDgYCADrz55s9ZuvQ1fHxab9/pmhrjLnTr\n1r3Bc+8XRHl457b6knlycmKDBVHs7Ozq7XU/3CsPDu6BojhIUQwrJt85IUSzKy0t5fTpJJNh6fz8\nfGO7vb09YWER95Yr1Wzi8fAuZ9XV1ffKLa4mKSkRgNDQQWg0K5k791ns7e1b9Z6e1JMWRLlzp8gk\ncdfumT9NjfH6l5uZHnNycmqu2xbNQBKzEOKpKIrC+fPnOXDgMImJCSQkxJGRkW6yf3fXroHMnTvf\n2BseMGDgI7fyLC6+w+bNG1m/PpYbN66jUqmYNm0GGs0qRowY1SaHc+9XFvP29qFv334Nnl9aWlrv\nkHp+fh4lJUVcv37zqWqM11/drOaY1BhveZKYhRBP5O7dEpKSEk16w0VFRcZ2R0dHhgwZVms7yyg6\ndOjY4HWzsy/y4YcfsG3bJ5SXl+Hs7MKyZdG8/vqKRu1S1p7crzHevXtQnbaHt7OsXWP8QQ+8bmnS\n/Py8J64x/vCs9Noz1qXGeNNJYhZCPJLBYODChSyT5UqZmRkmW29269ad6dOnExoaRmTkEEJCBjR6\nyZCiKJw8eYKYmNUcOPANiqLQuXMX3n77NyxevFQqNTWDJx1SLywsfGhpWf0FUc6dyyAlRfvY69Vf\nY7zucrP7Cd0aC6K0BEnMQgijO3eKSEpKNCbhpKREiovvGNudnZ0ZPnykcUg6IiLq3taYT1Z0oKqq\nis8/30Vs7BrS0lIAiIiIRKNZxcyZs2UtsJmo1Wp8fX3x9fVt8NyHa4zXVxClKTXGfX196dSpI56e\nPvUWRGkPNcYlMQvRTun1es6fP2dMwgkJcXWW+AQF9WDKlGnGesPBwf2farZvQUEBmzZtYMOGD8nJ\nuY1areaZZ+ai0axiyJChT3tLohU9qsb4o1RWVtbphT+YrW663OzHHy89dY3x2sesrca4JGYh2omi\nosJ7Cbjmv+TkRJOyji4urowePdbYE46IiGpUz6kxzp8/R2zsGnbs2IZWq8XNzZ0VK95k+XINgYHd\nmuU9hGVzcHBodI1xb29nzp270uw1xutbblZ7eN1SaoxLYhaiDdLr9WRknDX2hBMS4rh48YLJOb16\n9WbmzGeMG3j06xfcrL0KRVE4evQIMTH/4PDh7wAIDOzO669rWLhwCW5u7s32XqJtsbGxMSbM4OCQ\nx577YEg916TGeH2z1q9fv9boIfWHZ6PXt9yspWqMS2IWog3Iz88nMTHemIiTkhIpLy8ztru5uTN2\n7HjjkHR4eCReXt4tEotWq2XXrs9Yu3YNGRlnARg6dDgazSqmT59pVUOKwvKZDqk/WY1x081f6j4b\nz86+2Kga44/aevV3v/tVk+5JErMQVkan03H27Bni4x88G76/X/R9ffv2M6k33Lt3nxZPiLm5uXz0\n0Yds3Lie/Px8bG1tmT9/AStWrGLw4PAWfW8hGquxNcah5nft/iz1+hJ37WfjZ86kUVVVZfJ6ScxC\ntFG5ubkmE7RSUpIpLy83tnt4eDJ+/MRaM6Uj8fDwbLX40tPPsHHjWrZu3UpVVRWenp780z+9xbJl\n0XTq1LnV4hCiudna2uLv74+/v3+D596vMV47eTf5fZv8SiFEs6uqqiI9Pa3Ws+F4rl69YmxXqVT0\n6xdCZOSDwg69evVGrVa3apwGg4FDh74lJmYNx459D0CPHj2Jjl7JCy8sxMXFpVXjEcLcatcY79mz\n4RrjjyOJWQgzunnzJgcOHDH2iFNSktFqH2za4O3tzeTJU42zpMPDI8w6aaqsrIzPPtvGhx9+wIUL\nWQCMHj2WX/3qbaKiRrf6BwQh2iJJzEK0ksrKStLSUoxLlhIT47l+/ZqxXa1WExIywFjUISpqCEFB\nPS1iE4Vbt26yYUPN8+M7d+5gb2/PCy8sRKNZxYABoU+8wYho3wwGA0eOvI9a/Q22tgVUVvbAx+dl\nwsLmmDs0iyCJWYgWcuPGdRIT442TtFJTT5tMDvH19WX27NmEhoYRERHF4MHhuLq6mjHiulJSkomJ\nWc0XX+xGp9Ph4+PDL3/5K1599XUCAgLMHZ6wUt988w7z53+Ih8f9I9mkpcWRkFBFZOQCc4ZmEZqU\nmHU6Hb/73e+4ceMG1dXVrFixggkTJjR3bEJYDa1WS2pqisme0rdu3TS229jY0L9/qMmz4e7dg/D3\nd7e4nqZer2f//m+IjV3NqVM/AjWzvDWaVTz77PPtqkSgXq+noqK8Rdaqtlc5OTfo0WN3raRcIzS0\nhLS0DYAk5iYl5r179+Ll5cVf//pXiouLmTt3riRm0W4oisL169dMZkqnpaVSXV1tPMfPz5/p02cZ\n6w0PGhSGs7OzGaNuWGnpXbZu3cyHH8Zw5cplAMaPn4hGs4rx4ye2q8Sk0+k4ePDPuLjsx8Mjn4KC\nQNTq5xk37k1zh2b1zpw5wPPPF9Tb5uV1/t4uXm6tG5SFaVJinj59OtOmTQNqnhU8zd65Qli68vJy\nUlNPm6wbzs3NMbbb2toSGjrQ2BOOjBxC166BVpPIrl27yrp1sWzZspG7d0twdHRkyZJXiI5e2aja\nwG3Rvn1v8dJLG3kwOFDIjRvpHDliYPz4n5kzNKvn4dGV27fVdOpUdy/s8nJ3KWACqJSGtjV5jNLS\nUlauXMmLL77IjBkzmjMuIcxCURQuXbrEyZMnOXXqFCdPniQlJQWdTmc8p1OnTgwfPpzhw4czbNgw\nwsPDrXJ49+TJk7z//vvs3r0bvV5Phw4dWLVqFRqNBj8/P3OHZzY5OTfJyhrEqFH5ddr27AljzpwE\nmX3+FBRF4dNPR/Dii6dMjuv1sGuXhuefjzFTZJajyYn51q1bvPnmmyxevJh58+Y16jWW9iztSbWV\nmadyHw+UlpaSkpJca1g6nvz8PGO7vb09AwcONs6SjoiIatQm/I3V2t8LnU7H11/vJSZmNYmJ8QAM\nGDAQjWYlc+c+2+TN+9vCz9T9ezh+fCdTprxGfUuxjx93w9c3FR8fn9YPsJGs4XuRnZ3M+fM/Y9as\nFLy84MIFBw4fnsCUKRtwcXGxintoDD+/pg3JN2kMOj8/n2XLlvGnP/2JYcOGNemNhWhtNb3hi8TH\nxxmXK509e8akvFyXLl2ZM2c+ERGRREYOITR0kNkrzTSH4uI7bNmyifXrY7l+/RoqlYpp02ag0axi\nxIhRVjPs3ho6dOhLdrYToaEVddry8/0ICmrfzz+bQ48eYQQGHuH773dSUXGdDh2GMG/eGHOHZTGa\nlJhjY2MpKSlhzZo1rF69GpVKxbp167C3t2/u+IRostLSuyQlJRp7w4mJ8RQWFhrbHRwcjHtJ3+8R\nd+jQ0YwRN79Ll7L58MMP2Lp1C+XlZTg7O/Paa68THf1Gozb8b4969Qrlyy9HEhr6ncnxqiooKpog\nf+eaia2tLaNGvWjuMCzSUz1jflLWPjTRloZX2tp9GAwGLl68YFw3nJAQR2bmWZPKMIGB3Yybd0RG\nDqF//1Cz/5Ftie+FoiicPHmCmJjVHDjwDYqi0KlTZ5Yt07Bkyct4eno16/tB2/iZqn0PeXk3OXly\nFSNHnqB3by0JCR6kpU1h2rQ1Fj+C0ta+F9asVYeyhTC3kpJikpNPcujQ0XtlDhO4c+eOsd3JyYlh\nw0bUKuwQ1eY3xKiqquKLL3YTE7OatLQUAMLCwlmx4k1mzZojs12fgJ9fJ2bP3kNGRgLJyWfo23cU\nc+bICINoHZKYhcUzGAycP3/OZN3w+fPnTHrD3bsHMWnSVOOQdHBw/3aTiAoLC9i06SPWr19LTs5t\n1Go1s2bNQaNZxZAhQ+X58VMIDo4kODjS3GGIdkYSs7A4RUWFJCUlGNcNJyUlcvduibHd2dmFkSNH\nM3r0SEJCamZM+/r6mjFi88jKOk9s7Bp27NhGRUUFrq5uaDQrWb58Bd26dTd3eEKIJpLELMxKr9eT\nmZlh0hu+X7Xovp49ezF9+kzjs+Hg4BBsbW3bzHOoJ6EoCkePHiE2djWHDh0Eap6dL1+uYdGipWat\nPCWEaB6SmEWrKigoIDHxwZrhpKREyspKje2urm6MHj2OqKiaJBweHom3t+WuGW0tWq2W3bt3EBu7\nhoyMdACGDBmGRrOK6dNnyu57QrQh8tssWoxOpyMj46yxsENCQhyXLmWbnNOnT1/j5KzIyCH07dsP\nGxsbM0VseXJzc/n443V8/PF68vPzsLGxYd68Z9FoVhEeLs8+hWiLJDGLZpOXl2ccjk5MjCc5OYny\n8jJju7u7B+PHTzQm4fDwiBZZutMWnD2bztq1a9i581Oqqqrw8PDkzTd/wbJl0c2685gQwvJIYhZN\nUl1dTXp6mkm94fsViQBUKhX9+gUbk3Bk5BB69eoteww/hsFg4PDhg8TErOGHH44AEBTUg+jolbzw\nwkKLq9VsbuXl5Zw9ewIPjw707h1q7nCEaDaSmEWj5OTcJiHhQW84JSWZiooHWxZ6enoyceJkYxIO\nCwvH3d3jMVcU95WXl/PZZ9v48MMPyMo6D8CoUWPQaFYxefJU+TBTj8OH/wsnp80MG5ZNfr49+/YN\nJTj43+neXRK0sH6SmEUdVVVVnDmTalLY4dq1q8Z2tVpNv34hxlrDkZFD6Nmzl6yXfUK3b9/i/ff/\njZiYGIqKirCzs+P5519Co1lFaOhAc4dnsX78cTMjRvwbXbtWAeDvX0VIyDE2b15Bp05HzL6bmxBP\nSxKz4NatmyQkxBmHpFNTT98rVl7Dx8eHKVOmGXfRCgsLx9VVNvJvqtTU08TErOaLL3ZTXV2Nt7c3\nv/zlO7z66usEBHQwd3gWr7x8tzEp1zZ3bhoHDmxl7NhXWj8oIZqRJOZ2RqvVcvLkGQ4e/N44Uevm\nzRvGdhsbG/r3DyUiItL4fDgoqIf0hp+SXq/nwIF9xMau5uTJE0DNjPS33/5npk6dY5X1nM3FwSG3\n3uNublBdfa2VoxGi+UlibsMUReH69WsmM6VTU1Oorq42nuPr68e0aTONw9KDBoXhUl8hWtEkpaWl\nbN++hbVrP+Dy5UsAjB8/EY1mJePHT8Lf390iN0nRarUcPfoednYnUakMaLVhjBz5Nu7unuYODa22\nM5BW53h+vgonp76tH5AQzUwScxtSUVFBSspp45rhxMR4cnJuG9ttbW0ZMCCU0aNHERIyiMjIIQQG\ndpPecAu4fv0a69bFsmXLRkpKinF0dGTJkld4/fU36Ncv2NzhPZZOp+Prr19i2bJD3N9u3GA4xscf\nn2L8+M/NPjvc13cJ6ekn6N//wQcaRYEvvhjCzJnPmjEyIZqHJGYrpSgKV69eMUnCZ86kodPpjOcE\nBHRg5szZxiHpQYMG4+Tk1C63smwtCQlxxMau4auvvkCv1+Pn58+vf/17Xn55mdn3887KOs3ly59i\nY6PF3n4Yw4c/V+9mLidObGbRogdJGUCthqVL4/j0038wZcpvWjHqusLCnuHUqTucObOenj3PUlTk\nyo0bIxk27N/NtjmNoij88MNH6HQHsbHRUlERwtChv8Db288s8QjrJonZSpSVlZGSkmyyZCkv78Gz\nNjs7OwYNGmyybrhz5y7SG24FNT3MvcTErCYxMR6A/v1D0WhWMm/ecxZRv/fQof+iT5//YuHCmu1P\n8/M3sGPHTp55Zkud+HS6ONzqmdtnawt2dsmtEW6Dhg1bgqIs5tatm/To4crgweZdmrd378+YP38T\n3t41Fc8U5RBbt35PWNgO/Pw6mTU2YX0kMVsgRVG4dCnb+Gw4ISGes2fPoNfrjed06tSZ2bPn3UvE\nUYSGDsLR0dGMUbc/JSXFbNmyiXXrYrh+vWbS0ZQp01ix4k1GjhxtMR+Krlw5T/fufyc8/MGe5L6+\nCsuWHWDHjv+iQ4eh5ORsxc4uj6qqLuTnlzzyWgaD5fyMqVQqOnXqbO4wOHv2FKNGfWZMygAqFSxc\nmMYnn7zH1Kl/M2N0whpJYrYApaWlnD6dZDIsXVBQYGx3cHAgPDzSWGs4IiLKIv4gtVeXLmWzbl0M\nW3uYrDUAACAASURBVLduoaysFGdnZ159dTnR0W/Qs2dvc4dXx7lz21m4sLjOcXt7KC/fQUDAaiZO\nfPBo4+hRL/butWX2bJ3J+fn5KuzsJrV4vNbmxo19jB1bUee4SgWOjpYxwiCsiyTmVqYoChcvXjD2\nhBMT48nISMdgMBjP6do1kDFjxhnXDQ8YMFA2TTAzRVH46aeTfPDBP9i//2sURaFjx0689dbbLFny\nCl5e3uYO8ZHU6ioe1XlXq28wYIDW5NjYsUWsXt2Z1NQiBg4sB+DiRXsOH36ROXMWt3S4VkdRbFEU\n6v03VhS7ugeFaIAk5hZ2924JSUmJxp5wYmI8RUVFxnYnJyeGDBlmTMKRkVGyyYQFqaqqYu/ePcTG\nriElpab3M3hwGBrNKmbPnoedneX/4fX3n8KFC7H06lVpclxRwM5OW+9rBg8u5urVLaSnfw/o8fef\nzty5Y1o+WCsUErKIkyc/ZMSIOybHdTqorBxhpqiENZPE3IwMBgNZWedN1g1nZmagKA+ePXXr1p0J\nEyYbt7IMCRlgFX/c25uiokI2bfqI9evXcvv2LdRqNTNnzkajWcXQocMs5vlxYwwcOIbdu5/F13cr\nnveWISsKrFvXg/Dw7Hpfo9Xa0a9fJB4eMnTdkC5denD48C9ITv4vwsJqHgkUFsJnn01kxox3zByd\nsEaSmJ/CnTtFJCUlGGdKJyUlUlLy4Fmes7MzI0aMqlXmMBJ/f38zRiwacuFCFrGxa/jss61UVFTg\n4uJKdPQbLF++gu7dg8wdXpPNnbuGgwcjMBgOoVZXUFERyujRPyMp6QUiIhLrnH/r1jAGDjT/ZiLW\nYsKEX5KVNZ5PPtmOra0We/shzJ37osnyLb1ez48/bqOq6iigwt5+LCNHviRFSkQdkpgbSa/Xk5aW\nxsGD3xsnad2vBHRfjx49mTp1unG5UnBwCLa28k9s6RRF4dixo8TGrubgwQNAzXP+5ctXsGjRkjZR\nJUutVjNu3OvA6ybHO3X6I1999TNmzLiKWg1VVbB7dwh9+75rnkCtWO/eYfTuHVZvm16vZ8+eV3nh\nhc/xvjcdoaBgO5999h3z56+X5CxMSNZ4hMLCgnu94Tji4+NJTk6ktPTBzFUXF1dGjx5HZGTNbOmI\niCH4+PiYMWLxpCorK9m9ewexsWs4e/YMAJGRQ3jjjTeZPn1Wu/hQ1b//BAoKjrBtWyy2trkYDEEM\nG/a62Xf3amtOnNjCwoWf41HrM56PD7zwwi6+/34io0fLpDrxQNv/y9MIOp2OzMyMWmUO47h48YLJ\nOb1792HkyGcZMCCMyMgh9O3bz2y7DImnk5eXx8cfr+Ojj9aRn5+HjY0Nc+fOR6NZRURElLnDa3U+\nPn5MmfIHc4fRpul0R02S8n3e3lBdfRSQxCweaJeJOT8/3zhD+v6z4fLyMmO7u7sH48ZNMM6SDg+P\nxMvLW7aytHIZGWdZu3YNO3d+SmVlJe7uHqxa9XOWLYumS5eu5g5PtGlKE9tEe9TmE7NOp+Ps2TPG\nWsMJCXHGKj9Qs3tQ3779TLay7N27jzzzaSMMBgNHjnxHTMxqjh49AkD37kFER7/Biy8uliFb0Sps\nbEZz9+6uOludFheDra0sQxOm2lxizs3NNRmSTklJpry83Nju4eHJhAmTjEk4PDyiTUzuEabKy8vZ\nsWM7a9euMU7SGzFiFBrNKqZMmWbxjyFKS+9y5swxvLw60rdv/ROKhPUYOXIpW7YcZPHir43JuaQE\nPvlkNvPnLzJvcMLiWHVirqqqIj09rVYijufq1SvGdrVaTb9+ISZbWfbs2Ut6w21YTs5tNmxYy8aN\nGygsLMTOzo4FC15kxYpVhIYOMnd4DVIUhYMH/y9eXtsYNeo6OTn27Ns3lODgv9K9e39zh9cuaLVa\nTp3aiU5XQUTEfLy8nn5Sp62tLXPnbubAgU3o9T+gKCpsbccwf/5Si/+QKFqfVSXmW7dumlRXSk09\njVb7YOcib29vJk+eauwNh4WF4+paT5kc0eakpaUQE7Oazz/fRXV1Nd7e3rz11tu8+urrdOjQ0dzh\nNdqxYx8yceL7dOhQs0+1l1cV/fodY9OmlXTpcqhdzBQ3p8TEXZSV/T9mzryAgwMcPvyfJCS8xuTJ\npqUus7KSuXTpE+zsiqiq6smwYW/g4eH12Gvb2toyduxr/P/27jwuynLv4/hnYBhA0FQEzCXczZ1Q\nK0+iuKDilhsqKpamgOLRk2Zlr/P0WCezV0+d53UWyMFdxEdKI5e0XDLLHTHNpSiXNNFcQBIQHGCu\n5w9Pk8SibHPPDL/36+UfXNcM8724ZH7MfV/3dcPUahyBcAQ2+1t+9+5dTp48UWRP6bS0y5Z+Jycn\n2rfvaNlBq1u37jRv3tKudmQSlVNYWMj27Z9iNMZw4MA+ANq0aUtExEzGjBlHrVq1NE5Yfvn5myxF\n+X7Dhn3Dl19uoGfP8RqkqhmuXLmEXv8qo0dfs7QFB//CxYvvc+RIG558chQABw6solGj15k48d4W\nnAUFsGHDZtq2XUuTJq00yS4ci80U5rS0y5YifPToEU6ePIHJZLL0N2jQgEGDBlsWaXXp8oQs3Kmh\nsrOzWb9+LcuXGzl37hwAQUF9iYqKJiion12fqjAYrpfYXq8e5Ob+ZN0wNczhw0sYMeJasXY/v7sc\nOJAEjCIz8xbwPt27/74vtl4P48efIT7+bZo0WWG9wMJhaVKY8/LyOHHieJE9pa9evfJ7KL2eDh06\n0a1bd0sh9vNrJp+Ga7i0tMssW2YkPn4Vt2//iqurKxMnTiYiYibt2rXXOl6VyMtrCqQWa09Lc6Ze\nvc7WD1SD6PW3Sr0LV17ej+zcOYRLl77hxRezS3yMh0cySil5nxKVZrXCvH79er74Yi8pKcmcPPkt\n+fn5lj4fH18GDx5mWaTVubO/XR6GFNUjJSUZozGGLVs2UVhYSIMG3rz88mvMmzcHnc5d63hVql69\nSXz33SHatfv9zV8p2LbtGZ59NkTDZI7P2bk9OTng4VG87+7ds0yZcoZt26C0AzI6nVkKs6gSVivM\nYWFhALi4uNCpU+f7bnP4JE2aNJX/zKKIgoICtm/fygcf/JujR48A0K5dB2bMmMXIkWNwdXV1yA1f\nunUbxcGD2Zw4sZJmzb4nM7M2V6/2pHfvd+V3pJr16xdBQsIapkw5WuST86ZNbgwceG+RaWAgfPEF\nDBxY/Pk5OQF2fRpF2I5KFeYTJ07w3nvvER8f/8DHvvfeezz+eBc6d+6Cm5tbZV5WOLDbt38lISGe\nZcuW8PPPlwAIDh5IZGQ0gYG9a0Rx6tFjMkqFc/36dXx9PejaVdZSWIOrqytPP51AfPxCatU6hF5v\n4s6dJ8jMPM6zz95beFq7Nuh0cOYMtP/P2ROl4JNPWtOmzSsapheOpMKFedmyZWzatAmPko77lGDe\nvHkO9+lGVJ2ffrrAsmVLWLduLdnZWbi7u/P88y8QETGTVq1aax3P6nQ6Hb6+vlrHqHG8vR8lJMSI\nUgqlFE5OTuzeHQz8fkXIgAFw/DgkJsKtW13w8Aiia9eZeHtrd1leRsZNUlJWo9PdoUOH4Tz6qO1f\nsy9KV+HC7OfnR0xMDC+//HJV5hE1iFKKw4cPYTTGsH37VsxmMw0bPsqcOXMJD3+e+vXlbl1CGzqd\nznJ0RqkQMjMPU/e+21P7+8OZM50YPvwLXFxcNEp5z6FD8bi4/I3x43/ByQl+/PFfJCUNZ/hwo2xe\nYqcqXJiDg4NJS0uryiyihsjPz2fz5iSMxhiOH/8GgM6d/YmKimb48JEYDAaNE4ry+O67Qxw6dICc\nHANPPfWcppv6pKVd4PTpVej1ORgMXenRY2yli1Pfvn8hKekKLVpsJDAwnRs3nNix4wlatXpX86J8\n48YvuLq+yYABv1/m1bp1Ho0afcjmze3p33+uhulEhalKuHz5sho3blxlvoWoQdLT09XixYtV48aN\nFaB0Op0aMWKE+uqrr5TZbNY6niin/Px8tXr1BPX99+5KKZTJhNq6tbk6ePAjTfLs3m1UX3/dQJnv\nLY5W6emoFSv6q+zs7Cr5/leuXFJbtsSqffu2qMLCwir5npX1ySdvqMJCy5H3Iv+Skvpomk1UXKVX\nZSv18Lcss/dzzI6yCtja4zh37kfi4j4gMXEdd+7cwcPDk+nTo5g2LYrmzVsAcPNmydeGlsUR5sOe\nx7BjxzuEhq7D/T9XrLm4wJAhF9i8eR7nz/egdu06Vsty61Y6JtN/07fvTUtb/fowefIuEhJeISRk\n8QO/x4PmQq+vy1NP3btvcnp6TqmPs6Y7dzJKvXyrsDDLbv9v2fPvxf28vSt29KjSa/trwipZUX5K\nKb7+ei+TJo2lR4+urFy5jPr1vVi4cBHHj59h0aJ3LUVZ2CcXly8sRfl+ISGXOHJklVWzHD26huDg\nX4q1OzuDm9sBq2axpnr1enLpUsmH03Nz21k5jagqlfrE3LhxY9avX19VWYQDuHv3LklJGzAaYzl9\n+iQAXbt2JyoqmiFDhstNGByIs3PJnxpdXECp21ZOY6K0U8lOTqaSOxxAQMAAPv54EFOmbMHV9ff2\nrVtb0q7dn7ULJipF3iVFlbh58yarVy9nxYql3LhxHWdnZ559dhSRkTPp1u1JreOJapCb+zhwslj7\n2bOu+Pr2tmqWli2HcezYPwgIKH5KJC/Pcbcy1el0DBu2ko8+eheD4SucnXOBAPz8onjssce1jicq\nSAqzqJTvv/+OuLhYNmxIJC8vjzp1HmHmzNlMmxZJkyZNtY4nqlGrVjPZvfsQ/fr9bGnLy4Pduwcz\nalSgVbO0aNGeLVvG4+e3Ai8vs6V906ZWtGv3olWzWJvBYGDgwL9avq7u87O3b/9KcvIGnJ31PPXU\nWNxLOp8hKkUKsyg3pRR79uxiyZIYvvzyCwCaNWtORMQMxo+fKPfAriFatuzK2bOrWLs2ljp1UsnL\nc8dkCmLYsFcf/ORqMHTo+3z5ZUcKCj7H2TmL3Nx2dO4cTaNGspahquzZ8w/q1PmAMWOuUFAA27f/\nLy4uL/PUUxO0juZQdKo8y6oryd5X2TnSSsGKjCM3N5ePPlpPXFwsP/xw7w5IPXo8Q1TULAYMGGT1\nzQwcYT4cYQzgGONwhDFA9Y3jm2924Of3HG3bFl1bsG+fF66u22nWrOoOnTvSXFSEfGIWD3Tt2i+s\nXLmUVauWk5GRgV6vZ8yYcURFRdO5s7/W8YQQVnDz5gYGDCi+4K9nz3QSElbRrNk7Vs/kqKQwi1Kd\nPPktRmMMSUkbyM/Pp169evzlLy8xdep0GjbUbl9gIYT1ubhklNGXacUkjk8KsyjCbDazY8dnGI0x\n7N//NQCtW7chImImoaHj5T7Zokrk5eVx8OBKlPqWmzdzMJkMNGzoQ8OGQ+jY8Rmt44kS5OW1RCn4\n49YVJhMUFNS8G81UJynMAoDs7GwSE9cRFxfLhQvnAejVqw8zZkTTp09/uc+sqDK//prB3r3jmDDh\nsGWDkhMn4OpVaNx4GZs3T2TYsL/bzeZFt2//yuHDy3B2zsBg6ESPHqEOefMIf/+ZbNnyOcOHny/S\nnpjYiZ49IzVK5ZikMNdwaWmXWb48jvj4Vfz6ayaurq5MmBBORMRM2rfvoHU84YD273+LqVMPF/nk\n1aULZGRAvXp5DBmykgMHevDMM2O1C/mQTp7cwe3b8xk79gJ6Pdy8CR9/vJo+fRKoW7e+1vGqVMOG\nfty5s4q1a9/Dw+MYZrMzOTlP8sQTr+PpKfcMr0pSmGuoY8eOYjTGsHnzJxQWFtKggTfz5y/g+een\n4e3trXU84cBq1TpS7HAoQO/esHUrDB9uJjf3c8C2C3N+fj7Xr7/O+PEXLG0NGsD06ftZs+avDB4c\nq2G66tGihT8tWqzFbDYXuTWmqFpSmGuQwsJCtm3byooVS9i/fz8A7dq1JzIymlGjQnFzc9M4oagJ\ndDpzKe3w28Wbev1dKyaqmMOHNzF48Jli7TodeHjsRynlsIVLTm1VLynMNUBW1m0SEtawbJmRS5cu\nAtCvXzBRUbPo1SvIYd88hG26c8cfOFWsPTkZnnji3mKi/HzbvwwvN/cWpR3BdXHJw2w2O+S5ZlH9\npDA7sEuXLrJ06RISEtaQnZ2Fu7s7kydPZcGC+Xh5NdY6nnAgGRk32L79ddzdv0EpJ+7efZrAwJfx\n8PAo9lh//5dJTPyGsWNPWw5pp6XBzz9Dt26wcuXT9O8/08ojKL8nnniWPXvepV+/a8X6cnI6SVEW\nFSaF2cEopThy5DBGYwzbtm3BbDbj69uQ2bNfZPLkKdSv7+Uwu+oI25CV9SuHDo0iPDzZUmgLCw+y\nfHkKQ4Z8jMFgKPL4Rx9thsGwifj4f2MwnOLKlcvk50OLFg1ISOhGnz7z7OKyvAYNfDh6dCK//PJP\nGjYssLTv29eQRo1s/w8LYbukMDuI/Px8tmz5BKMxhm++OQZAp05diIqK5tlnRxV7cxSiqhw48C/C\nwpKLLOhydoaJE7/i009X06fP9GLP8fLyISTkTSumrB4DB/43+/Y1w2TagsFwi9zcFjRrNp0OHZ56\n4HOVUmRnZ+Hm5o6LS8n3VBY1kxRmO5eZeYs1a1axYkUcV66kodPpGDRoCFFR0fTo8YycPxbVzmA4\nWeK9kD08QKkUoHhhdhQ6nY7AwOeB58v1vCNH1nP79gq8vVPJyalDRkYvgoLekRvACEAKs906f/4s\ncXEfsH59Anfu3KFWLQ+mTYtk2rQoWrRoqXU8UYMUFpZ+2z+zWVb6/1FKShLNms2jQ4ffTifdwmyO\nZ+nSa4watUHTbMI2SGG2I0op9u//GqMxhh07PkMpRZMmTZk//zUmTZrMI4/U1TqiqIHc3AZx/fom\nfHwKi7Snprrj6ztKo1S269atNQwaVHSNh5MTBAd/ybfffknnzkHaBBM2QwqzHTCZTCQlbcBojOXU\nqW8B6Nq1O1FR0QwZMhy9XqZRaOeZZ8axe/dxOndeRYcOdwBITq7NDz/MYMCAXhqnsz2urj+V2N6i\nhYlDh44CQVZMI2yRvKPbsPT0dFavXs6KFUu5fv0aTk5ODB8+ksjImXTv/uDFJUJYg06nIywshn37\nxrBu3RbAmVatQhkwoJ3W0WySyeQFnCvWnpEB7u5NrR9I2BwpzDYoNfV74uJi+eij9eTl5VG7dh1m\nzPgz06ZF0rTpY1rHE6JEbdt2o23bblrHsANDuHUrmXr1VJHWrVv9GTBgjEaZhC2RwmwjlFLs2bMb\nozGGPXt2A+Dn14yIiBmEhU2S1ZpCOIi+ff/C5s3XaNJkI4GB17h6Vc+XX3ajXbv/kU1JBCCFWXO5\nubls2JBIXFwsqanfA9CjxzNERkYzcGCI/KIK4WB0Oh2DB79Devo8Pvnkc7y8HiMkJFAubRQWUpg1\ncu3aNVauXMrq1ctJT09Hr9czevRYoqKi6dLlCa3jCSGqmZeXN336TNI6hrBBUpit7NSpkxiNMSQl\nbcBkMlGvXj3mzJnH1KnTefTRRlrHE0IIoTEpzFZgNpvZufNzjMYY9u37CoBWrVoTETGTsWPD7GJf\nYCGEENYhhbka5eTkkJi4jqVLP+DcubMABAYGERU1k379Bsg9TYUQQhQjhbkaXLmSxvLlccTHryQz\nMxODwUBY2CQiImbSoUNHreMJIYSwYVKYq9Dx48dYsiSGzZuTKCgooEGDBsyb9wpTpkzHx8dH63hC\nCCHsgBTmSiosLGT79k8xGmM4fPggAI8/3o7IyGhGjx6Lm5ts4i+EsG/Z2dkcPGhEr7+AydQAf//p\n+Po21jqWw5LCXEHZ2VmsWxdPXNwSLl36CYC+ffsTFTWL3r37yDWJQgiH8PPPqaSmPs+YMacxGEAp\n2LFjPVevvo+//xCt4zkkKczldOnSRZYtM5KQsIasrNu4ubkRHj6FyMiZtGnTVut4QghRpU6deoPJ\nk09bvtbpYODAKyQmvk1h4SDZBKkaSGF+CEopkpOPsGqVkY8//hiz2Yyvb0NmzZrD5MlT8fLy0jqi\nEEJUuZycHHx8jpTYFxR0kpSU3XTvPsDKqR6soKCAAwcSKCg4jNlswMdnhF3dTlMKcxny8/PZunUT\nRmMMx46lANCpUxciI2cyYsRoDAaDxgmFEKL6mM2F6PX5Jfa5uYHJdMfKiR4sLy+PTz+dwIQJu6hT\n517bjz8msH37DEJC3tQ23EOSwlyCX3/NJD5+NcuXG0lLu4xOp2PQoMG88sp82rcPkPPHQogaoXbt\nOly75g/sKda3Z09LunYdZP1QD/DVV//LCy/swsXl97bWre+SlxdHaupwu7gDmuxwcZ/z58+xYMFL\ndOnSjjff/C9u3brFCy9EcPDgMdasWU9QUJAUZSFEjdK48Yvs2VN0u+AzZzwxmyNt8qoTvf5gkaL8\nm06d7nDpUpL1A1VAhT4xK6VYuHAhqampGAwGFi1aRNOm9nmDb6UUBw7sw2iM4fPPt6OUonHjJrz0\n0quEhz/HI4/U1TqiEEJopkOHIC5c2MDatUtxc7vE3bte+PqOJzCwv9bRSuTkZC6jt8BqOSqjQoV5\n165dmEwm1q9fz4kTJ1i8eDGxsbFVna1amUwmkpI2EBf3ASdPngAgIKArUVGzGDJkOC4l/cklhBDV\nIC3tAqdOxWEwXMFkakTHjhE0btxc61gWzZt3pHnzf2gd46Hk5gZgNn/FH3c8Pn/egI+P7R16L0mF\nCnNKSgqBgYEAdOnShVOnTlVpqOqUnp7OmjUrWL48juvXr+Hk5MSwYSOIjIyme/cn5VC1EMKqTp7c\nRWHhLCZOvIJOd+864V27ksjI+DedOtnmp1Jb1rPnPFatOsDkyUfQ/6fCpafr2LVrLCNGBGma7WFV\nqDBnZ2dTu3bt37+JXo/ZbLbpmzL88EMqRmMsH330f+Tl5eHpWZvIyGimT4/iscf8tI4nhKiBlFJc\nvfouEydesbTpdBAcfIV1696lY8d+8mGhnGrXfoQ+fZJITPw3BsNxCgoMGAzBjBgRbjc/ywoVZk9P\nT3JycixfP2xR9vau/cDHVCWlFLt27eLvf/87n332GQDNmzdn9uzZTJ06lTq/raUvB2uPobrIOGyH\nI4wBHGMc1h7D2bM/4O9/tMS+Tp2OkpV1jZYtW5f7+9b0ufD2rk3z5m9XYRrrqlBhDggIYM+ePQwa\nNIjjx4/Tpk2bh3rejRtZFXm5csvLy2Pjxg+Ji4vlu+/OAPDUUz2IjIwmJGQIzs7O3L1b/jze3rWt\nNobqJOOwHY4wBnCMcWgxhvT0bDw9S+7T6eDmzWzq1Kl571OOMAao+B8XFSrMwcHB7N+/n/HjxwOw\nePHiCr14Vbt+/TorVy5l9erl3Lx5E71ez6hRoURFRePvH6B1PCFqjHPnvuXcudUYDBnk5fnRvXs0\nXl7eWseyOc2bt2LXrq506HC4WN/Jk13p16+lBqmE1ipUmHU6HW+88UZVZ6mwM2dOYzTGsHHjh5hM\nJurWrcvs2XOZOnU6jRrJHVCEsKbDh9fh5fUaEydmAGA2wyefbKZJk5U0b95F43S2RafT4eMzjz17\nZtOnzy+W9j17GuLtPc9uzomKqmW3O3+ZzWZ2797BkiWxfP31lwC0aNGSiIiZjBs3AQ8PD20DClED\nmUwmTKa/06NHhqXNyQlGjTrL2rXv0Lz5/2mYzjZ16TKIixe3sHbtMlxdr3L37qM8/vg0/Pzkpjg1\nld0V5pycHD788P9YuvQDzp79EYDAwN5ERs6kf/+BNr0yXAhHl5z8Kf37/1BiX/36R8nNzcXd3d3K\nqWyfn19b/Pz+R+sYwkbYTWG+evUKK1bcO3+cmZmJwWBg3LgJREZG07FjJ63jCSG4dyVEaUdf712j\nq6wbSAg7ZPOF+cSJb1iyJIZNmz6moKAALy8v5s59mSlTpuPr66t1PCHEfbp3H8KuXa0ZOfLHYn0Z\nGQHUqlVLg1RC2BebLMyFhYV89tk2jMYYDh06AEDbto8TGRnN6NFj5VCYEDbK1dUVJ6fZHD36X3Tr\nlgnc28lq8+YWtGz5isbphLAPNlWYs7OzWLcunqVLl3Dx4k8A9O3bn8jIaIKC+soKRSHswJ/+9Byp\nqe1JSFiLwZBBbq4fAQEz8PWVKySEeBg2UZgvXbrIsmVGEhLWkJV1Gzc3N8LDnyciYiZt2z6udTwh\nRDm1bdudtm27ax1DCLukaWFOTj6M0RjL1q2bMJvN+Pj4Eh09m+eeewEvLy8towkhhBCasHphLigo\nYOvWTRiNMaSk3NsjtmPHzkRGzmTEiNG4urpaO5IQQghhM6xWmDMzM4mJiWH5ciOXL/+MTqdj4MAQ\noqJm8ac/9ZTzx0IIIQRWLMxNmzYlOzubWrVqMXXqdCIiZtCiRStrvbwQQghhF6xWmOvWrcuLL75M\nePhz1K1bz1ovK4QQQtgVqxXm8+fPk5mZZ62XE0IIIeyS1TaWdnFxsdZLCSGEEHZL7vgghBBC2BAp\nzEIIIYQNkcIshBBC2BApzEIIIYQNkcIshBBC2BApzEIIIYQNkcIshBBC2BApzEIIIYQNkcIshBBC\n2BApzEIIIYQNkcIshBBC2BApzEIIIYQNkcIshBBC2BApzEIIIYQNkcIshBBC2BApzEIIIYQNkcIs\nhBBC2BApzEIIIYQNkcIshBBC2BApzEIIIYQNkcIshBBC2BApzEIIIYQNqVRh3rlzJ/PmzauqLEII\nIUSNp6/oExctWsT+/ftp165dVeYRQggharQKf2IOCAhg4cKFVRhFCCGEEA/8xLxhwwZWr15dpG3x\n4sWEhIRw5MiRagsmhBBC1EQ6pZSq6JOPHDlCYmIi77//flVmEkIIIWosWZUthBBC2BApzEIIIYQN\nqdShbCGEEEJULfnELIQQQtgQKcxCCCGEDZHCLIQQQtgQKcxCCCGEDanwlpwPY+fOnXz22WclXuf8\n4YcfkpiYiIuLC1FRUQQFBVVnlAq5e/cu8+fPJz09HU9PT9555x3q1atX5DGLFi3i2LFjeHh4EE60\nrQAABXVJREFUABAbG4unp6cWcYtQSrFw4UJSU1MxGAwsWrSIpk2bWvq/+OILYmNj0ev1jB49mtDQ\nUA3Tlu5B41i1ahUbNmygfv36ALz55ps0a9ZMo7RlO3HiBO+99x7x8fFF2u1lLn5T2jjsZS4KCgp4\n7bXXSEtLIz8/n6ioKPr27Wvpt4f5eNAY7GUuzGYzf/3rX7lw4QJOTk688cYbtGrVytJvD3MBDx5H\nuedDVZO33npLhYSEqLlz5xbru3Hjhho6dKjKz89XWVlZaujQocpkMlVXlApbuXKl+te//qWUUurT\nTz9Vb731VrHHhIWFqVu3blk72gPt2LFDvfrqq0oppY4fP65mzJhh6cvPz1fBwcEqKytLmUwmNXr0\naJWenq5V1DKVNQ6llHrppZfU6dOntYhWLkuXLlVDhw5V48aNK9JuT3OhVOnjUMp+5mLjxo3q7bff\nVkoplZmZqYKCgix99jIfZY1BKfuZi507d6rXXntNKaXU4cOH7fZ9qqxxKFX++ai2Q9ll7aX97bff\n0rVrV/R6PZ6enjRr1ozU1NTqilJhKSkp9OrVC4BevXpx8ODBIv1KKS5evMjrr79OWFgYGzdu1CJm\niVJSUggMDASgS5cunDp1ytJ37tw5/Pz88PT0xMXFha5du5KcnKxV1DKVNQ6A06dPYzQamTBhAnFx\ncVpEfCh+fn7ExMQUa7enuYDSxwH2MxchISHMmTMHuPdJR6///cChvcxHWWMA+5mL/v3787e//Q2A\ntLQ0HnnkEUufvcwFlD0OKP98VPpQdkX20s7OzqZ27dqWr2vVqkVWVlZlo1RKSeNo0KCB5bC0h4cH\n2dnZRfrv3LlDeHg4U6ZMoaCggMmTJ9OpUyfatGljtdyl+ePPWK/XYzabcXJyKtbn4eGh+c+/NGWN\nA2DIkCFMnDgRT09PoqOj2bt3L71799YqbqmCg4NJS0sr1m5PcwGljwPsZy7c3d2Bez/7OXPm8OKL\nL1r67GU+yhoD2M9cADg5OfHqq6+ya9cu/vnPf1ra7WUuflPaOKD881HpwjxmzBjGjBlTrud4enoW\nKXI5OTnUqVOnslEqpaRx/PnPfyYnJwe4l/H+/yRw75cjPDwcV1dXXF1defrpp/n+++9tojB7enpa\nsgNFipkt/vxLU9Y4AJ577jnLH0+9e/fmzJkzNvsGVBJ7mosHsae5uHr1KrNmzWLSpEkMHjzY0m5P\n81HaGMC+5gLgnXfeIT09ndDQULZt24abm5tdzcVvShoHlH8+NFmV3blzZ1JSUjCZTGRlZXH+/Hla\nt26tRZQyBQQEsHfvXgD27t1Lt27divRfuHCBsLAwlFLk5+eTkpJChw4dtIhazP3Zjx8/XuSPhZYt\nW3Lx4kVu376NyWQiOTkZf39/raKWqaxxZGdnM3ToUHJzc1FKcejQIZv5+ZdG/WGjPXuai/v9cRz2\nNBc3b97khRdeYP78+YwcObJIn73MR1ljsKe52LRpk+XQrqurK05OTpY/vO1lLqDscVRkPqp1VfYf\nrVq1Cj8/P/r06UN4eDgTJkxAKcXcuXMxGAzWjPJQwsLCeOWVV5gwYQIGg8Gyuvz+cYwYMYLQ0FBc\nXFwYOXIkLVu21Dj1PcHBwezfv5/x48cD904vbN26ldzcXEJDQ1mwYAFTp05FKUVoaCg+Pj4aJy7Z\ng8Yxd+5cy1GLHj16WNYE2CqdTgdgl3Nxv5LGYS9zYTQauX37NrGxscTExKDT6Rg7dqxdzceDxmAv\nczFgwAAWLFjApEmTLCvNd+zYYVdzAQ8eR3nnQ/bKFkIIIWyIbDAihBBC2BApzEIIIYQNkcIshBBC\n2BApzEIIIYQNkcIshBBC2BApzEIIIYQNkcIshBBC2JD/B1byrV8rvj7oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105f46a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(-1, 3.5)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "\n",
    "for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:\n",
    "    plt.plot(xfit, m * xfit + b, '-k')\n",
    "\n",
    "plt.xlim(-1, 3.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are three *very* different separaters which perfectly discriminate between these samples. Depending on which you choose, a new data point will be classified almost entirely differently!\n",
    "\n",
    "How can we improve on this?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Support Vector Machines: Maximizing the *Margin*\n",
    "\n",
    "Support vector machines are one way to address this.\n",
    "What support vector machined do is to not only draw a line, but consider a *region* about the line of some given width.  Here's an example of what it might look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XIDs7B4CQQyGGG10qlUKlUkGpVAfVTTkJMzFqyFyWjasxV/FM9zP99unS9STK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110bacda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(-1, 3.5)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "\n",
    "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n",
    "    yfit = m * xfit + b\n",
    "    plt.plot(xfit, yfit, '-k')\n",
    "    plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none', color='#AAAAAA', alpha=0.4)\n",
    "\n",
    "plt.xlim(-1, 3.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice here that if we want to maximize this width, the middle fit is clearly the best.\n",
    "This is the intuition of **support vector machines**, which optimize a linear discriminant model in conjunction with a **margin** representing the perpendicular distance between the datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting a Support Vector Machine\n",
    "\n",
    "Now we'll fit a Support Vector Machine Classifier to these points. While the mathematical details of the likelihood model are interesting, we'll let you read about those elsewhere. Instead, we'll just treat the scikit-learn algorithm as a black box which accomplishes the above task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape=None, degree=3, gamma='auto', kernel='linear',\n",
       "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC  # \"Support Vector Classifier\"\n",
    "clf = SVC(kernel='linear')\n",
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To better visualize what's happening here, let's create a quick convenience function that will plot SVM decision boundaries for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_svc_decision_function(clf, ax=None):\n",
    "    \"\"\"Plot the decision function for a 2D SVC\"\"\"\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    x = np.linspace(plt.xlim()[0], plt.xlim()[1], 30)\n",
    "    y = np.linspace(plt.ylim()[0], plt.ylim()[1], 30)\n",
    "    Y, X = np.meshgrid(y, x)\n",
    "    P = np.zeros_like(X)\n",
    "    for i, xi in enumerate(x):\n",
    "        for j, yj in enumerate(y):\n",
    "            P[i, j] = clf.decision_function([[xi, yj]])\n",
    "    # plot the margins\n",
    "    ax.contour(X, Y, P, colors='k',\n",
    "               levels=[-1, 0, 1], alpha=0.5,\n",
    "               linestyles=['--', '-', '--'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jPZGYmuSDqIkCB2c7U62qtsK7A4PB7tbEH3qwm1dv4Ni/DyM8PwQVOjMiHo5C7/H9fB2W\n0/X8Aty8eB2tu7VFRKR48Y5r5/Nx5se5mHp6CoIQBAECtsZtg/1PQK+H+3g1NovFggPf7IXdYkff\nhwcgNDS0Xq/j7w55sJ9ZakRuOLLmIErfL0KHE+1QoanA5b756PDbzmjVubWvQ2syLp28gBs/voqH\nL/4IClSVKl3UXsSBnx8JmHKeDU+swbxvZovav+z4FQZ/N9Jrz8MPfr0PprcNGJM3GhposLnlZpif\nqsSwp7Me+Fr+7pAH+7nu5MtnviRy9sBpRLwSilkHZ6CXuReGlA/B3O8excWfnIXBIL1eMTXcuXfO\nYOLFh52JFwBam1sj9pNIlBaX+DCy+rFYLIg6JL2P8uizo3Bw0wGvXPfq+SsI+S8tpuRNRihCEYxg\nTMifgE5/bo/j24955ZpEnsbkSyJXF11CvxLx3riTzz6CA5/u8UFEvmM2m7H+N2uwfegm7O75HTbP\nWIfcb4965L11uVrJ9hGFw3F45UGPXMObHA4HVJXSk6+CEQyb0TtLUp75/ASGFg8RtXeqyEDhCumS\nMCJ/wwlXJKK9Lr3xehCCoMwP7KUFG2r906vwxIb50OCH4dMCIOfYQZz4Zy66ZknXwtZbLf/1VaIS\nqiD/n1Gs0+lQ2u028J342Oa0Legzob9Xrqsp07iMFrgcK+WvNAoMvPMlEUus9B2LHXbY4ypljsZ3\nTu49jpFbR9xLvD/oW9YHNz6pe2u/+jD2NorKeQBgU8tN6DdtYKPfXw6pz7fG5pTNLm1nQs7C+mMH\n9HrvLD5S2doBG2yidgECzGncAIICA78mkkj8jCSc3HIKXco7u7SvbfUN+i6o38L8gebahXyc/CAX\n2itBsEVWInZKPIpyb2GERXrTBP1F6SHjhsh8bQA+O/s5ZubOgBZV77cnci+EX6gREhLS6PeXQ8cB\nGbi6/AoWf7gMwVeCYI22I25KAoaNfPDEJ3cNeHIwVqz+GrNOu5Z6bUzdiG5P9/TadYk8qVHJt6Sk\nBFOmTMEnn3yCVq1aeSom8rFuWT2w5/WdOPPhWQw42w8GjQEHex5G2mttER4hPcEmkJ07eBblz5Rg\nbv4sZ9uZDWdxeGQOKlCBEIgToS1cfOfVULGJsRixeixWffoNQq4G466mAu3ndMKADl0b/d5ySm2f\nhtS/psl2vdDQMHT8qBsWvbUULQ6FQFmpQnmPCqS/0AZJ6cmyxUHUGG4nX7vdjtdffx1abePvAMj/\nDJo3FLZZNlw/fxEmmwNjuv4o4LeSq83ldy5gdr7rXVRGRUecP3oBX7VfgfnnHnM5ZoABdg8tbKXX\n6zHyp2NYltFAKW1aIuXDlrDb7RAEockt8UlNn9vPfP/yl79g1qxZiIuL82Q85Ec0Gg16D+2Njt0y\nmmzitVqtaJErvTjD6Pxs3B5TjqWdl+E2bkOAgAPhB7B89lcY+fPRMkdKUtRqNRMvBSS3ku/KlSsR\nHR2NQYMGQaY1Ooi8QqlUwqGWnkRmgw2pndMwYvNYbPvXHix74yuoN4Rg4t+ncks9ImoUt4adV65c\nCYVCgT179uDs2bN45ZVX8M9//hPR0dGejo/Iq9RqNe72rgDWiI9tbLcJAyYMh1qtxuDJQ+UPjoia\nrEYvLzl37lz84Q9/eOCEK7u9Emq1/9cuUvOTn5ePvVP34pHjjzjXJ94Vvwuqv6swaJb0bGciosZo\ndKlRfZ8FlpUZG3spF5ygIo/m0M/aiAj0XTUUX3+8BsrzgC3Kji7zuyM5PUW2zx5I/Xz5+0vIW3UW\nUAAdp3RGyzapvg6pQQKprwMZ+5kbK1AjsJ/lESj9vOHNtcj4rB363O0DAQJywnNwfsFljH51vK9D\nq7dA6etAx37mxgpE5AGHN+Vg6PsD0edu1VaBCijQ704/9HsvE8e2HvFxdESBhStcEQWgyspK7Pjg\nO2CHAyqLCsbOZvR9biCi47036bF0bTHSrSNF7W0tbZGz5jDgvUWtiJocJl+iACMIAlY/twKzv56J\nUFTVKAu7BSzbvRw9l/VHTEKMV66rNtX+66KuY0QkxmFnogCTu/0oxqzNdiZeoGoIeNapmTj07n6v\nXdfWyS65oYEFFti7NJ8NN4g8gV9XiQJM8bZCjLIOE7UroID2RJDXrjvw6aFY8u1SPHZ0nnNLPwEC\nlvReipELAmfClRRBELD931vg2FIJTbkK5nYWtHs6A626tPF1aNREMfkSBRhHUO0FCnUda6zQ0FAM\nXDIci/53GfRHgiFAgKm3FUN/me217QPl8s3L/8Ejnz+MSCGyquEIsHnvZlz4wIE2vdr5Njhqkph8\niQJMh+mdsP+z/eh/x3WzegsssA/w7vBvZEwUxr31I69eQ26Xzl5E95Vd7yXeH4zKH4XF/1yGNh8w\n+ZLn8ZkvUYBJa5+OKz+7jkNhh51tN5U38fHYTzHihVE+jCwwnd94DpnlvSSP6U5y1zbyDt75EgWg\nrOdH4WL2BSz98guoLCqEDAzDlAmzmuzuU96kClXBCiuCIH5e7tBzIhl5B5MvEYA9i3bC9JUB2mvB\nsMZY4RivxMgXRvt1MmvdqQ1a/54Tghqr36yBWP+vDZh0daJLux12GAdYfBQVNXVMvtTs7fpwO3q9\n0RXplvSqhmtAWW4Z1pSuxfg/POzT2Mj7QkJCoP1tCNa/vh5jboyBCircUN7A6uHfYNxr/Pcn72Dy\npWbN4XDAvtxyL/H+IFKIRMKqWNx+sQwRkZHSL6YmI3NSP5QNKcUXn62E8i4Q1icck8fP8OuRD6pS\nWVkJi8UiOePeZDJhx45tMJtNMJnu/S84OAg//vEzPoj2HiZfataKioqQer6l5LH+N/th+759GDie\n2wo2B5HRURj1i7G+DqPZEgQBFosFZrMJFosV8fHxonPMZjPWrPkPzGYzTCYjzGYzLBYLdDo9fvaz\nn0u+7/Hjx5z/X6vVQqfTITS09g0P5MLkS81aWFgYrkR8D0jseJmvzUdcWpz8QREFOLvdjvLycty6\ndQtmswlWqxVt24pLtqxWKxYt+gQmkxlmswkOhwMAoNFo8OKLvxKdr1arcfnyJajVauh0erRoEQ6d\nToeQkBDJOLRaLRYseBo6nQ5arRZKpf8U+DD5kl/Kv3gVV45fRuuebZCUluy16+j1etwaUgLHFw4o\n76u8O9T/CB7q/IjXrk3k7wRBcLnLNJmMMJnMsFjMyMzsIzrf4XDg3XffhtVqRUhIMCoqqiasKRQK\nvPTSK6Lkp9FoYDZboNUGIzIy8oc7Uz20Wi0EQRAN+6vVarz44q+g0WjqFb9CoUB0tPc2G2kMJl/y\nK4bycmx9YRO67uiCUeXDcDL8JNZk7UP238d7bRWl4X/Kxkdln2DYziFob26PAlUBvu2zGb3+0v/B\nLyZ6gMKCmzj+5VFAADpN7ork9BSfxnPr1q0fkqjJ5Vno8OFZkneG7733f8470pq6deshSoJKpRJx\ncfFQqVRISIiG1Sq4JNP7KRQKPPvs8w2Kv76J198pBKke8QJPb6rMjZrlIXc/r31qJeavmutyF2qH\nHZ/PXIIfvTvZq9c+nXMSBYfyEdUuBr2ye8s62YY/z/KRs6+/e+dbJLwfg2ElQwEA+8L34eLjVzHm\ntYc8do2LF8+jouJeMq1OqOPGTUBQkLh2+d1334bZbBa1P/fczyW/4K5btxZKpdJ5V6rTVf3ZunUb\nqNW137/xZ7qqD2rDO1/yG0W3itBmeyvR8K8aaiRvTcTdu3fQokW4167fqW8XdOrbxWvvT83Lyb3H\n0fWdDHQ2dnK2DbwzEIkLE3Go1wH0HttP8nUnTuSivLzcOcRbnUwnT54m+Wxz48YNMBjESW748CzJ\n5Fs9XFxziFen0yE4OFgynocealrLifoLJl/yGzcuF6DD7daSx1JvtURR0S2vJl8id1VWVkKpVLqM\nltxYeQ0jjIOwG7tRilKYYIIRRpisJuz52z60G9AB4eERovfav38vysrKXNpUKhXMZrNk8h0ypOqu\nWqvV/TCxqOrP2h7TDBo0pDEflTyEyZf8RquM1jiZdAIp18XPxM6l56FnEp/BknfVLHcJDQ2THFbd\ntu07FBcXuTwztVgsmD//x4iLuzc7Xl1R9dqTOImbuOls10KLILsGNptdMobs7DEAqiYDVt+dajSa\nWh+DdO3a3e3PS77D5Et+IyysBW6OL0bFhxUIwb1v+LdxG3cmVECn0/kwOgo0drsdZrMJRmNVkoyL\ni4dWK94oYcOGdbh+/Zqo3GXOnMeQlCSeaX/9egEKCq6Jyl3uT46VnRywfG3BZEyGEkrooYcWWggQ\nsHTsl4iJiZGMu1Ur6dEfalqYfMmvjH1zAr4OXoPQTTok3IzH9aQbMD9kxZhXAnuzdnLf/eUu1Qk1\nPT1dcrGE1atX4tKli7BarS7tM2Y8irS0dNH5BkM5jEYTdDqtS7lLUJD0M9BHHpkKjUbzwFm3AxcM\nxZJ1S/H4kflQoCoxCxCwtMtyDHiGQ7/NHZMv+RWVSoVxr0+A7TUbbt++jfSIDk2mtICqVFRUwGAw\nOIdsq//s0KEjoqLENZkrVnyBS5cuitqnTJkmmXy1Wh0iI6Og1WqdQ7darQ5hYdIzT6dObdgykvUt\nedPr9Ri8OAuL/mcZ9Ie0gAMw9TKj10v9EB4hftZLzQuTL/kljUaD2NhYX4dB9VBcXIzbt8uc9aLV\n5S7duvVAQkKi6Pxvv92AvLxzovbIyCjJ5JucnAK1Wg2tVudS7hITI/3zMWbMuAbF782SssiYKIz7\nC2cLkxiTLxG5uHYtH7duFbqsaGQ2m5CZ2UfyeeS+fXtw5swpUXtiYpJk8m3dug3CwsKcZS7Vs3Pj\n4sRr+QLAwIGDG/+hiPwMky9REyG1HB9QtQhDfn6+aEWjAQMGISOjk+j8U6dOIjf3qKi9des2ksk3\nI6MT4uLiodfrXMpdWrRoIRln9+493fh0RE0Lky+Rn6kud1EqlZKLJJw5cxrnz+e5TEAymUwYMmQY\nevXqLTr/8uVLOHTooEubVquFxSJe5QgAunbthtTUNJdnptXlLlLatm0nuWg+EdWOyZfIi2qWu+h0\nWoSFie8GT5zIxeXL53DrVpnz7tThcGDo0BHo33+A6PyiolvOYd6a5S4ajThRA0CPHr3QoUNGjbvS\nund3SUpKliyxISLPYfKlgGO327Ht3c1Q71JCZVLC3NmKzj/tjuQ23luwXqrcJSwsXHJS2NGjh3Hg\nwD6YzWaXcpcBAwZhyJBhovMrKiqQn5+PykqlS7lLeLj0al6ZmX3Qo0fPOu9Ga5KaxEREvsXkSwFF\nEASseuYrzF8zFzr8sOjGEeA/+1YBi1CvBGy322EyGZ2LL1TfbUZFRSM1NU10/qFDOdi27TvRriy9\ne/dFVla26Pzq567V5S46XdUdZ2JikmQ8ffr0w4QJo1FcbHhg7ABq3buUiAIHky8FlOM7jmHcxtH3\nEi8AI4zofT4Ty9/6Epkv9Hcm1Li4eHTsmCF6j9zco/juu82i9h49ekom37CwFkhOTrlvIXo9kpKk\nk2mPHr3Qo0even8mlUol6w5KROR7TL7kd+7evYOCggLRikaJiYko21mCbOtQl/PP4izWYA1O55zB\nrQ3FzvZOnbpIJt+YmFhkZHR2zs6tTqbR0dLL/XXo0BEdOnT07IckombN7eTrcDjw29/+FpcuXYJS\nqcQbb7yBtm3bejI2aiJKS0uQl5cnWtEoKSkZw4aNEJ1fUFCAtWtXidrtdhv0Wh0ECM7l+gAgEYkY\njMFQxqoxeNxw58Si2kpd0tLSJZcZJCKSi9vJd+vWrVAoFFi2bBlycnLw9ttvY+HChZ6MjXxIEARU\nVlZKHisqKkJu7hGYTK4TkJKSUjBhwsOi80tLS7Fjx1ZRe23L9CUmJmLUqDHOu9Ka5S5lfcuw7dPt\nyCq+l7QTkYgIRODWQ6Xc4YWIAoLbyTc7OxtZWVkAqu5UapuZSb5XXe7icDgk98O9desW9uzZ6Vx8\nofruNDU1Dc8++5To/IoKA44cOez8e3W5S23lKwkJiZg8eZrLXqN1lbtERESiZ89MyWPxSfE4//JZ\nfPfXrcgqHgEFFLgcdBkbx27GxOen1qc7iIh8rlHPfJVKJV599VVs2bIF7777rqdiolpUl7tUD9sC\nkKzHLCwm6zUhAAAgAElEQVQsxMaN65x3pdXlLikpLfHoo3NF59tsVuTlnYNCofghOVaVu9S25Vli\nYhIee2yB85npg8pdQkNDPboIw6D5w1A4uhDLFn8FhVmB2KHxmDysYYvjExH5kkK4v37CDSUlJZg2\nbRrWr18vuV8mANjtlVCrVY29VJNhs9lgMplgNBqdfyqVSmRkiCcIFRYW4rPPPoPJZHIpd0lMTMTT\nTz8tef5HH30EnU4HvV7v/DMuLg5Dhw4VnV9ZWQmr1QqtVssERkQkA7fvfFevXo3CwkI89dRTCA4O\nhlKprHPVnLIyo7uXkhQbG4aionKPvqe7Kisrcfv2bZd1c81mE5RKJTIz+4jOLyoqwieffCBqj4qK\nQkyMuE61vNwKh0OJiIhYl3KXyMhIyT5QKvV48smfScZaV58ZDOI6U3/q56aM/Swf9rU82M9VfVAb\nt5Pv6NGj8etf/xpz5syB3W7Hb37zG8l1aAOR3W5Hfv5VlyFes9kEhUKJESNGis4vL7+Ljz56X9Qe\nFtZCMvnq9Xq0atXaOcRbnUyl9iYFgPDwCCxYIL7DJSKiwOR28tXpdHjnnXc8GYvX2Gw2nD17WrSi\nEQBMmjRFdL7FYsFXXy0XtWu1Osnkq9eHoFu3Hs4JRdXPQmubzRsSEoJp02Y28lMREVFDCYIAm812\n30ilGWq1WtYNQgJykQ273Y7t27fjxo1i516jJlPVbN758xeIzhcEARs2rBO1q9VqyW3YdDodBg8e\n6jLEW13uIiUoKAhjx473zIcjIqJ6cTgczuRZPcG0eg/qmn+v+vPejZfdbhe9V1xcPJPvgyiVSmzf\nvh0VFRZnW3W5i8PhED171mg0GDdugnON3ZrlLlITjJRKJTfwJiKSiSAIsFqtkony3p/ihGo2S2+L\nKUWr1UKr1SI2Ns55Y6XTaWssyiNvuWzAJt/58+fDYLDXq9xFoVCga9duMkZIRNQ8VVZW/lCZYcK1\na0XO5Fn92K9m8jQa7y3SU9uiPvdTq9XQanUIDQ1DXFy8aM31mvNo7v2pq3NCsC8EZPIFgPT09GY/\nk46IyFsEQYDFYql1OLfmM9Oad6nV6wqEhAS7jE7eT6FQIDhYC71eh/Dw8Acmz+pRS41G0yRKIgM2\n+RIRUf1Ub6NZn+RZfZdqsZjhcDjq9f4ajQY6nQ4REZHOOTLx8VGwWiE5xFu9dKy/3Y3KicmXiChA\nOBwOUQmk1LPQmsO5JpMJNputXu9fvcqdXq9DVFSUyxyZ6nkyUkO8arU4lbDOt25MvkREMnMtd5Ga\nmSu+S62+G63vooRBQUHQ6XSIiop2Js+ad51SQ7zBwcFNYkg3EDD5EhE1Qn3KXaSGeKXKXaQolUro\ndHqEhIQgNjb2h1m79xJp9aTT+ys5pO5GyX/wX4eICPfKXep6FurpcpfakmfNId6goCDejTZBTL5E\n1ORUl7tIJc/gYODmzVKPlLuEhbV4YLlLzYTanCcYkSsmXyLyW+JyF6mE6nqXajabYbHUXuJSswSm\nutxFp9PWWu5SM3k2tXIX8h0mXyKSRc1yl7qSZ827VLPZ1KByF61Wh/DwCJclYWsmUb1eh+TkWBiN\nlSx3IZ9i8iWiBhEEweUusz5r6bpb7hIZGekyQ/f+hFqzfrSuVe5qYgkM+QMmX6Jmqr7lLlKLL7hT\n7lJX8qx5d1rbmutETQmTL1ETUFe5S11DvO6Uu8TExNxX1iI1Y7cqkbLchUga/8sg8iN1lbvUNcTr\nTrlLTExsrcnz/rtUlrsQeRaTL5GX1FXucn/yVKkcKCq63aByF5VKBZ1OX+fuLlKLL6hUKi9/ciJ6\nECZfogdoSLlLzYRaV7lLTQqFAtHR4QgK0ojKXaQWX2C5C1HgY/KlZqW+5S73PzNtbLlLXc9HtVot\n4uPDOQOXqBlh8qWAFOjlLkTUvDH5kk8JgiC51yjLXYioKWPyJY+Rs9yleneX+1cvYrkLEQUC/lYi\nkZrlLjZbOa5dK6rXdmmN2d2lPhOMWO5CRE0Fk28Td3+5S32fj1aXu9RchF7K/bu73L/4wv2bdVf9\nyd1diKh5Y/INENXlLg3da7Qh5S7BwVro9TqEh4c7k2dCQhSsVtQ5wYh3o0REDcPk6wN2u905cehB\ntaLulrvodFXlLvdvzF3XBCOpu1EuQk9E5HlMvo0gCEK9noW6W+6iVCqdQ7c1y13ufxbKchciosDC\n5Iv67O4iHuJtaLlLcHAwtFotoqKiRcmztuejwcHBHNIlImqCmlzyrS53aegEI0+Uu9Q1Y5fr6RIR\n+Z7NZoPVakVISIhP4wjI5Gu327FhwwbcuFHikmDd3d2F5S5ERIHF4XA4H+/ZbDbExyeIzqmoqMDa\ntaucN1vV54aFtcBPfvKcD6K+JyCTr1KpRE5ODgyGqkRbW7lLbZOLqpMpy12IiHyr+rFfzRFJm82G\ndu3ai841mUxYvPhTmExml8d+Wq0Ozz//ouh8lUqFq1evIDg4GDqdDtHRMdBqtQgLa+H1z/UgAZt8\nn3nmGRgMNpa7EBH5gNlsxq5d/we1eh+ASlgsmRg06EUoleofHumV/bBAjwkWiwW9e/cVvYfVasU/\n/vF30TaaarUaL774K9Hv9aCgIFitNoSGhiI2tuZ+1HrJGIODg/HSS6/45WM/t5Kv3W7Ha6+9hoKC\nAthsNjzzzDPIysrydGx1io+Ph1LJEhgiIm8RBAGFhTdhNLrOlzEaK3DnzvtYsOA7BAVVnetw7MBH\nH+3BqVODodFoRAv09OrVWzTaqNFokJCQ+MP6666jlFJUKhWeffb5esevUCj8MvECbibfNWvWIDIy\nEn/9619x584dTJo0SfbkS0TkCfn5V2G1WtCqVZtm8SgqL+8cjMYKUVnkww8/Ipmoli5dJJqQeuXK\nMbz33r3ECwBKJTB//gH86lcp6N59OhITo2E2C87HfFIUCgVmz57n0c8XKNxKvuPGjcPYsWMBVD30\n5sL1RBRozp07gEuX/hudOh1AixY2bNvWHRERP0Nm5hRfh9Ygx44dgcFgqHFXWvXnzJmzERwcLDp/\nw4Z1MJtNonaTyYTQ0FCXNoVCgb59+0OlUtWYQ6PD4cPnEB0tjkWjAQYONGHEiHFcoOcB3Mqa1d9i\nDAYDXnjhBbz4ovhBNxGRv7p9uxSFhc9gzpwLzrZOnY4gJ+eXOHs2GR079vfq9W02G9RqteRclT17\nduHOnTsud6VGowmPP74AoaFhovP37duL8vK7Lm1BQUEwm02SyXfEiCwoFErJddelDB48VNSWl9cC\ntQ0SOBzia5KY27esN27cwHPPPYc5c+Zg/PjxDzw/MlIPtdqzY++xseIfRPI89rM82M/yOXXqU0yc\neEHU3rdvCVauXIohQ0bV632qy12MRiMiIiIkRwHXr1+PoqIimEwmGI1G52ze559/HlFRUaLz8/Mv\noKSkBED1ugI6xMVFIiJCh8hI8c/InDkznOfp9VV3pnWNRmZlDa7XZ6tL27azcOnSUrRqZXVpLy1V\nIDp6gvNnmT/TtXMr+RYXF2PBggX43e9+h/796/cNsazM6M6lasUhDXmwn+XBfpZPbGwYLJZLqPl4\nUxAAmw0wmYDi4nM4ePA4EhOTJO8c165dhZs3b4jKXR57bAHi4+NF558+nYfCwpvOchetNgwREVoU\nF5ejslK8FGx29gSoVErRKnd2OyR/RsLCYp3/32yG5JCyp6WnD8D69U/DaPwInTtX/W6/dCkImzdP\nx6RJU1FUVM6fadT95cOt5Pv+++/j7t27WLhwId577z0oFAp8+OGHCKr59J2IyAfuX+Wu+s9Wrdo4\nn2na7YmorARUKmDxYuDSJaC62uX48bvIy1uG2bPnITk5RfT+RqNRstwlKEh6TfUZMx6FRqOp96zb\nmJgY9z64zMaP/yPOnp2IpUv/A6ASsbFjMWnSCJZ91pNCqO/ixI3k6W9A/FYlD/azPNjPtSsvv4uK\nigpRuUunTp0RGSketl22bDHy86+K2qdPn4X09FaIjQ3DuXOXcerUSDzyyEWsXg3cugXodMD166EA\nXkGHDpno3LkLwsMjZPiETRN/pr1w50tE5K7CwkLcuXNbtOZ6r16ZkksEbtq0ARcvip/PxsXFSybf\nli1TodfrRZuWRNeYnhsZGY3Y2H9iyZI30aVLDjp2tOHYse7o0uU59Okz3bMfmEgCky8RNcqVK5dR\nVHTrvkUYjBgwYBBSU9NE5+/fvwfff39W1J6Wli6ZfNu2beeyG1h1Uo2NjZOMR2p2rpQOHQagQ4f1\nuHz5IgwGE4YPz2gWdb7kH5h8iZopQRAkn8/l5Z1Dfv7V+zYsMWHw4GHo0KGj6PyTJ0/g1KkTovZO\nnToDECffTp26IDk5RbSNZm3r7fbo0avhH64B0tNbe/X9iaQw+RIFuOpyF5VKJTk79+TJE7hwIe+H\niUf3dnfJyspG9+49RedfunQBx44ddf5dqVRCq9XBZrNJXr9Hj55o27ZdjXV2q/6srdxFasF8ouaG\nyZfIT9y/u4ter5e8Gzx69DBOnTrpfGZaXe6SlZUtuXh9UdEt5zBvzd1dgoKkF0Po3bsvunbt7lx8\noWa5ixSpGcFEVDcmXyIvkCp3iYiIRGxsrOjcgwcP4MyZXBQX33ZZQ3fo0OHo33+g6PyKigoUFt6E\nVqtzKXepbWZuv34D0KdPP+h0unqVu0RFSawbSEQexeRL9AA2mw0VFQaXdXPNZhNiY+PQsmWq6Pz9\n+/di587tovb+/QciNna4qF2pVEKj0SA2Ns5ldq7U5CMAGDhwMAYNGlLvesratlsjIt9h8qVmx2Aw\noLS0xDmhqLrcJSkpWXJC0ZEjh7Fjx1ZRe+/efSSTb3h4BFJT01xm5mq1OiQnJ0vGk5nZB2PHZtW7\nJrK5zcgtKyvBgQP/gE53HhZLGBISpqNbtxG+DouoUZh8KeDdvl2GgoIC57PS6j9TUlqiZ89M0fl5\ned9j8+ZNovbu3XtKJt+4uDh07tzVWepSnUyjo6VXIsrI6ISMjE6N/2CEgoLz+P772Zg9+4xzIf8z\nZ1Zh27ZXMGLEz30bHFEjMPmS3ykuLsb58+dEKxqlpqZhyJBhovPz8/OxYcM3Eu+kkEy+iYlJGDBg\nkMsQr06nR4sW0qUurVq1RqtWLEfxhRMn/oy5c8+4tGVkVCA/fyHKyuYiMpLPpykwMfmSRzgcDtjt\ndsn1vQsLbyI396hzAlJ1yUt6eiuMG/eQ6Pzi4iLRM1OlUomIiEjJaycnJ2PMmHEuQ7zV5S5SEhIS\nkZCQ2PAPSbLT6w9Lto8ceRNffrkc2dnPyhwRkWcw+ZKLmuUugPTapDduXMeePbtqzOStKndp06Yt\nJk+eJjrfYCh3qRsNDg6GVquFRiP945eS0hJTp874IZE+uNwlKiqaM3Q9qLDwGo4cWQit9hpsthi0\naTMfbdp081E00v/mVSvSN69n39S0MPk2YfeXuyiVSiQliSf9XL9egI0b1zuHeCt/2N4lLS0dzz33\ntOh8m82GixcvQKVSuZS7xMSIy2gAICUlFU888dQPifTB5S6hoaHO3WdIXufOHUBZ2VOYO/cSqr/r\n7N37Hxw8+BefrHlsNPYBcF7UvmVLEvr0mSl7PESewuQbAARBgMVigdlscil3UavVaN++g+j869cL\nsGLFFzCbzS7tyckpmD17nuh8hUIBg6EcOp0OYWHxzqHb2tbOTU5OwQsvvISgoKB6lbsEBwdLrrxE\n8jGZTNi79wMolcdRWRmKhISp6NJFvKn6lSt/waOPXnJpGziwBF999XfY7ZPr3KTdG3r2/A0WLz6J\nmTNPoPrSx46FoaLiBYSHSz+G8Ibr1y/i+PF/QKc7Dbs9BArFSAwf/pNmN/OcPIfJ1wfsdjvKyspc\nZueaTGZoNGpkZvYRnV9YeBOff/6JqD02Nk4y+QYHV62TGxcX71LuEhkp/csqMTEJzz//i3rHr1Kp\n6r03Kfne7dul2LlzGubMOYjq70CnTi3Hd9+9hJEjfwWg6gve3bt3EB8v/Yx12LBTOHRoG/r0GSVX\n2ACA+PhUDBy4AV98sRBBQXmwWsOQmvoohg4Vr+TlLdeuncOVK7Mwd26es+3OnS348svTmDTpPdni\noKaFydcDrFYrrl27CqPR5Lw7NZmMUKs1GDFipOj827dv45NPPhC1R0ZGSibf0NBQtGnT1plEq/8X\nFia9V2R0dDQef/zHjf9g1CTs2/dHPPHEQdQcpOjc2YiSkvfw9dcGREbugFZ7AwZDAkpKzMjKAu4f\n0JBn129pYWEtMHr0qz67/unT72D27DyXtvBwYODAr/H994+jQ4fePoqMAhmTrwSr1YrTp0+6DPFW\nJVM1Jk6cLDrfZDJixYovRe2hoWGSyTc0NBQ9e/YS7TcaEiL9nDM0NAxTpnCPUXKPXn9QlEwBYMiQ\nUly79nfMmFHdcgMFBcC6dcCECa7n7tzZGYMHN8+FLbRa8Y5NQNUXmGXLNjL5kluaVPKtbYs0q9WK\n/fv3ip6ZKhQKPPbYE6Lz7XY7vv12o6i9ttIVvT4EQ4cOF61opNdLn6/VajFq1NgGfjoidzlqPRIS\n4vr35GRgxw41LBa7c4h6794YhIS8KPvzXn/hcEjPV3A4AEHgXAZyT0D+12Sz2bBy5UoUFpa6lLsI\nggMvvPCS6HyFQoH9+/e6tAUHByMkJEQyYWu1Wjz00MOiFY1qmzSk0WgkF8An8gcmUyYE4bjo7vfA\nAaBHD/H5PXpU4t135yEt7S6s1li0a/c4+vTpIk+wfshsHgybLQcajWv7li3x6NnzMd8ERQEvIJOv\nWq3GiRMnYDCYXcpddDodHA6HaAaiRqPBo4/OhVarq1e5i1KpROfOzfeXDTUtmZmvYPHiI3j00VxU\n/9hfvqxBTo4Czz9vFZ1/40Y0Jk16s9ZFTZqb4cNfxUcfncKkSZuRkOCAIAA7d0bDaHwVMTH3KgJu\n3LiCkye/gVYbjf79p0Bzf7YmqkEhCPJMpajvovH1FRTkQHm5rd7lLuSe2Ngwj//bkZi3+/nu3dvY\nt+//ITi4qlQmPPxhFBYuxfz561zuiAUB+PTTqZgw4WOvxeJr7vS1IAjIyVkNg2EfKitD0KXLPCQl\npTuPrVv3Mtq1+xKDBpWhogJYvz4DMTFvomvX0V74BIGBvzukFymqFrDJl/+w8mA/y8MX/VxSUojd\nu59CVtYetG5txblzWuzYMRQjRvwb4eFRssYiJ0/39bZtC5Gd/WtERbn+Kl25shV69tzTbBeM4e+O\nupMvK8SJmqno6HhMnLgaly6txNKlf8aNG2swadKKJp14vcHh2CBKvAAwYcIlHDjQdEcQqHEC8pkv\nEXlOt25DAQz1dRgBS6O5LdletcdImayxUODgnS8RUSOYzW0l269fV6FFC/GWlkQAky+R3yopKcK3\n376F7757Bbt3L3VueEH+JS3tKezeneDSVlkJrFkzDL17i7fMJAI47Ezkl44cWQ2H41XMmlUApRIo\nLQVWrFiErKwlfCbbSDabDVu3vg9gDwBAoRiMIUOeEC0iYrPZYDCUIzw8os4NFDp0GIBTp/6NJUsW\nQq8/Bbtdj4qKwRgz5k1WYlCtONuZ6sR+lkfNfjabzThwYBCmTnVdT1gQgM8/n4/x49/1RYhNgt1u\nx4YN8zFjxhrn6l4GA7Bo0UOYNGkR1Go1rFYrNm9+DeHhWxAdXYKbN9MAzMCIET974PvXtspec8Tf\nHXXPduadL5Gf2b//Czz0UJ6oXaEA9Pq9Eq+g+tq161NMm7bGZVnN0FBg9ux1+PbbRRg27HFs2PAc\n5s1b/sOEKQA4juvXz2D7dgWGD3+uzvdn4qX64jNfIj9jsxmgk14WHGq1WfoA1YvDsQdSm4G1aAHc\nvLkEX301A+3bf10j8VZJSrLB4fgSDkft62QTNQSTL5Gf6dbtEezcGS15zGTqJnM0TU3tv/JiYnLQ\nuvUGDBhgkzweG3sFBkPzHkYlz2HyJfIz8fFJuHJlDgoLXZ8Kbd2agrS0530UVdOg0QxHmUTpbUkJ\nEBsLpKYCFy5Iv/b27Rjo9SHSB4kaqFHJNzc3F3PnzvVULET0g7Fj/4A9e/6O5cvH4uuvB2DJktkI\nCVmK9u37+zq0gDZ48GysXj0DxcX32oqKgLVrgREjgE6dgMOHxa8zmwGDYUyz3VaRPM/tn6QPP/wQ\nq1evRsj9G4ISUaMpFAoMGfIYAG5Z50lKpRLz5i3FmjXZMJu3QRCACxcK8dpr36G6mmjUKGDJEqBn\nT6BVK+DQoSicOzce48a9IWusx4/vwK1bGwAokJw8ERkZ/OLVlLh955uWlob33nvPk7EQEXmdUqnE\noEEzMHLkv5Cd/S8MHPgLnD+vdR6PiwNmz65aKOPPf/4RIiJ24eGHF8q2RaAgCFi9+nmkp0/BrFkL\nMWvWe4iNnYh1616V5fokD7fvfEeNGoWCggJPxkJEASIv7zAuXfocwcFFMBpT0LXr00hJaSPb9S9e\nzMW5c/+GXn8RNlskQkImon//GW69V9euQ7B27TzodB+jZUs7AKCiAtizZwQWLPgQutqmnnvJnj1f\n4OGHP0dc3L2Z1RkZJuh0H+Dw4eHIzBwrazzkHbI9wIiM1EOtrn0De3fUVcBMnsN+lkeg9POuXYug\n072I2bNLAFQt/rF163qo1Z+ha9fhXr/+yZM7YTbPwdy5+c62goJvsXfvVUyc+Id6vcf9ff344//C\n3r3jcejQKiiVNgQFDcATTzyJoPtrjmSgUGx1SbzV0tNtOHZsE2Jjp8kek7sC5WfaFxqdfOu7QFZZ\nmbGxl3LB1VPkwX6WR6D0s81mw82bf8a0aSXONoUCGDnyKpYu/QMSEry/kcDx43/Go4/mu7QlJ1tx\n5sy/ce7cE4iMlC7TqlZbX7dvn4X27bOcf79zxwLA4pGYG8Jqraj1mNlsCIifEyBwfqa9yav7+XJF\nF6Lm4/jxnRg69LTksZSUwygtLZE85ikOhwN6fa7ksREjCnH48EqvXl8OdnsvWK3idoMBUKn6yR8Q\neUWjkm9ycjKWL1/uqViIyM8plSrY7dLHHA5lnRsQeIJCoUBlZbDkMZMJCAoK/GHOQYN+gs8+G4Ca\ni2nZ7cDixSMwcOA83wVGHsWiNSKqt27dhmDnzq6YPv2E6Ni1a33QuXOkV6+vUChgMPSHIFzC/YNu\nGzZ0wMCBk716fTno9XpkZ3+FJUveRnDwYQiCEjZbP4wf/6LHn0GXlJSgrKwEqanpPnm+3Zwx+RJR\nvalUKoSHv4zt23+JYcMKoVAADgewZk1rtGnza1li6NfvTXz88QVMn56DsLCq62/alITw8P9qMgkk\nNLQFxo79vdfev7S0CHv3/gLp6TuRmFiGnJwOsFpnIivrJa9dk1xxS0GqE/tZHoHWz1ev5uHMmQ8R\nHFwMs7klevf+KWJi4mS7vs1mw969i+FwnIbNFoFevZ6s9/UDra89TRAErFo1EU8+ud1l9KCgQIMD\nB97CkCFPeeQ6zb2fAW4pSEQelpraDqmpf/HZ9TUaDYYNe9xn1w9kx49vx+jRe0XD9snJNlitKwB4\nJvlS3bixAhFRM3Lr1nGkp0tMpwYQHMyFk+TCO18i8jqLxYLt2/8HQUG7YTDko6hIQFRUEoKDeyEz\n8wXExSX7OsRmIyamC/Lz1c7VvGqyWBJ9EFHzxORLRF7lcDiwdu1cLFiw0WWT+lWrrqFv3xzs3r0T\nDscXSEhI812Qtbj3pWEPVCorTKZu6NHjF4iPb+nr0NzWo0cW1qwZgAULdrkMPRcWqqBSTfJdYM0M\nky8RedXBg2swefK3uH8i8sSJwMqVwPTpp7Fkyd+RkPCObwKshfSXhoP44ov9UCq/Rmxski/Dc5tC\nocDAgR/g009fQocOO5GSUo6jR1ujomI6srOf9XV4zQaf+RKRVxkMexEfL16rWKEAqjcKCg4+KnNU\nD3bgwH8wZcom0ZeG6dNP4fDh//NNUB4SG5uECROWISzsIC5c2IqePfdh1KjXuGKhjHjnS0ReVVmp\ngyBANLsWgHMVJ4dDetUqXzKZ9iEuTlyJqVAAOt1JH0TkeQkJSUhICMw7+EDH5EtEbisouISTJz9E\nUFAJbLY09Ov3DMLDXVe5ysiYi717P8WgQWUu7eXlVXe+djtgsQyUM+x6sdm0tR6rrNTLGAk1RRx2\nJiK3HDmyGqWlYzB79j8wffpSzJjxFo4eHYPLl0+5nNeyZVvcvPkqtm2LQfWSPufOAatWAX36AB98\nMBLDhr3ig09Qt/btZ+PAgXBR+507gEKRJfEKovrjCldUJ/azPAKtn+12O3btGorp08XDr4sWjcfY\nseINVwoLryE393PcvXsd5eVGpKVFIDi4HwYMmOb1DRlqakhfb9/+D8TH/w1DhpRBoQDy8oKxbdsU\nTJy4sM6YzWYzKioqEBUV1Wyfowbaz7Q3cIUrIvKoI0e+w/Dh0s89Y2MPwmAwIDQ01KU9Pj4Fo0e/\nJkd4HjN8+M9w/fqPsHTpYiiVNiQmjsYjjwyq9XyD4S62b38FsbE7EBFxB8ePt0dQ0DwMGsTVuMgV\nky8RNZjdbhXNAq6mVldCEMSzmwNVUlI6kpJ+W69zN29+Aj/+8be4d1N8GOfOnUFOjg59+870WowU\nePjMl4garFevUdi2rZ3ksVu3eiIsrIXMEfneiRO7kJW1HfePRrdvb8Tdu4t9ExT5LSZfImowrVYL\nheKnOH7cNclu2dISKSnNc1u6mzcPoW3b2tZMviJzNOTvOOxMRG4ZNGgBTp5sj6VLlyIoqBhmcxoy\nMp5EamoHX4fmEy1atMGtWwrJ2mCbLdYHEZE/Y/IlIrd16TIEXboM8XUYfqFPnwlYt643Hn/8oEt7\naakCgjDBR1GRv+KwMxGRByiVSnTvvhCffjoU584FwWAANm9OwNq1zyIr60Vfh0d+hne+REQe0rJl\nB7Rs+Q3OnDmMU6cuo3Pn4ejRI9rXYZEfYvIlIvKwjIxMAJm+DoP8GIediYiIZMbkS0REJDMmXyIi\nIpAMNIwAAAkaSURBVJkx+RIREcmME66IiJoJk8mE7dvfhE63GyqVCSZTF7Rt+zxat+7p69CaHSZf\nIqJmQBAErFs3B08+uRlq52/+7/Htt4dw+fJSpKd39WV4zQ6HnYmImoGDB7/BpEnf1Ui8VUaPvoKz\nZ9/zTVC1KCi4jIMHN6O0tMTXoXgNky8RUTNQXn4AiYnSWz3q9edkjkba3btlWLt2Dszmwejbdwqu\nXeuPb755AXa73deheRyHnYmImgGHIwwOB0RbHgKAzeYfW0Bu3/4snnjiGygUVX8fObIQJtMn+Oor\nPcaNe8u3wXkY73yJiJqBzMwF2LQpUdR++zagUGT7ICJXV66cQ/fu252Jt5pOB4SFbYDVKr1dY6By\nK/kKgoDXX38dM2fOxLx585Cfn+/puIiIyIOiomIA/DfWrEmFzVbVdvRoGL7+ej5GjHjWp7EBQH7+\nSXToYJA8Fh9/C3fu3JE5Iu9ya9h5y5YtsFqtWL58OXJzc/HWW29h4cKFno6NiCigFRffxMGD/w86\nXR6s1jBER09GZuZ4n8XTu/c0GAxjsXLlYlRWGtCmzUN4+OFOPounprZt+yA3NxKDB5eJjl2/noJW\nrSJ9EJX3uJV8Dx8+jCFDqvbw7N69O06ePOnRoIiIAt21a3k4f3425s496xxKvXBhDTZv/gVGjXrV\nZ3GFhoYhK+snPrt+bRISWiInZwz69VsOjeZee2mpAlbrI1DfP007wLn1aQwGA8LCwu69iVoNh8MB\npdSTfCKiZujUqb9izpyzLm1t2phx9eoHKCqaj9jYBB9F5r/GjPkHlizRIyZmM5KTb+HSpTSYzY8g\nO9t3X1a8xa3kGxoaioqKCuff65N4IyP1UKtV7lyuVrGxYQ8+iRqN/SwP9rN85OjrsLCjku3DhhXh\nm29Wo1OnX3o9Bl9reD+HYf78j2A0GlFSUoLOneMRFBTkldh8za3k26tXL2zbtg1jx47FsWPH0L59\n+we+pqzM6M6lahUbG4aionKPvieJsZ/l0VT6ubz8LvLzLyI5OR3h4RG+DkeSXH1ttysk2x0OwGis\nbBL/3nVpbD9rtRG4c8cCwOK5oGRW15cPt5LvqFGjsGfPHsycORMA8NZbTav+iogaxmazYdOml5GU\ntB7t29/A+fPxyM8fjdGj30ZwcLCvw/OJioq+EITvRaUzW7YkoXfvWb4JivyGW8lXoVDgjTfe8HQs\nRBSgNm16BbNmfQStturvrVoVwmZbhEWLBPzoR82zEqJPn//CZ5+dwqxZR1D9/ePQoRYwmX6B8PCm\nNXOXGq5pTR8jItkZDAbEx290Jt5qGg2QmvotyspKERkZ5ZvgfCgmJgEjRqzHypX/hkp1FjZbGFq1\nehSDB3MHIWLyJaJGunnzBlq3viZ5rEOHW8jLy0NkZD+Zo/IPer0e2dk/93UY5IdYG0REjZKQkIiL\nF1Mkj507F4+UlHYyR0Tk/5h8iahRQkNDUVg4Dmaza7vVCly5MrpZDjkTPQiHnYmo0caM+TOWLROQ\nmLge7dpdx4ULCSgoGIPRo//m69CI/BKTLxE1mkajwYQJb6O8/PcoKLiKNm1aomfPcF+HReS3mHyJ\nyGPCwlqgY8cuvg6DyO/xmS8REZHMmHyJiIhkxuRLREQkMyZfIiIimTH5EhERyYzJl4iISGZMvkRE\nRDJj8iUiIpIZky8REZHMmHyJiIhkxuRLREQkMyZfIiIimTH5EhERyYzJl4iISGZMvkRERDJj8iUi\nIpIZky8REZHMmHyJiIhkxuRLREQkMyZfIiIimTH5EhERyYzJl4iISGZMvkRERDJj8iUiIpIZky8R\nEZHMGpV8N2/ejJdeeslTsRARETULandf+Mc//hF79uxBRkaGJ+MhIiJq8ty+8+3Vqxd+//vfezAU\nIiKi5uGBd74rVqzAZ5995tL21ltvYdy4ccjJyfFaYERERE2VQhAEwd0X5+Tk4IsvvsD//u//PvBc\nu70SarXK3UsRERE1GW4/822osjKjR98vNjYMRUXlHn1PEmM/y4P9LB/2tTzYz1V9UBuWGhEREcms\nUXe+ffv2Rd++fT0VCxERUbPAO18iIiKZMfkSERHJjMmXiIhIZky+REREMmPyJSIikhmTLxERkcyY\nfImIiGTG5EtERCQzJl8iIiKZMfkSERHJrFG7GhEREVHD8c6XiIhIZky+REREMmPyJSIikhmTLxER\nkcyYfImIiGTG5EtERCSzgE++mzdvxksvveTrMJocQRDw+uuvY+bMmZg3bx7y8/N9HVKTlpubi7lz\n5/o6jCbLbrfj5ZdfxuzZszF9+nRs3brV1yE1SQ6HA6+99hpmzZqF2bNn4/z5874OyW+pfR1AY/zx\nj3/Enj17kJGR4etQmpwtW7bAarVi+fLlyM3NxVtvvYWFCxf6Oqwm6cMPP8Tq1asREhLi61CarDVr\n1iAyMhJ//etfcefOHUyaNAlZWVm+DqvJ2bp1KxQKBZYtW4acnBy8/fbb/L1Ri4C+8+3Vqxd+//vf\n+zqMJunw4cMYMmQIAKB79+44efKkjyNqutLS0vDee+/5Oowmbdy4cXjhhRcAVN2dqdUBfd/ht7Kz\ns/Hmm28CAAoKChAeHu7jiPxXQPwErlixAp999plL21tvvYVx48YhJyfHR1E1bQaDAWFhYc6/q9Vq\nOBwOKJUB/X3NL40aNQoFBf+/vTtGURgIozj+ksIo5BweIHeIhZ0QwSKdrSAWAcULWAsRDLmEjVWa\nFOm9hNjERrCz2ELYai2d0dn/r0v3GMK85CtmzrZjOK3X60l6vtfz+VyLxcJyInf5vq/lcqmqqrTd\nbm3H+VhfUb5JkihJEtsx/pUwDHW/33+fKV58u8vlotlspjRNNRwObcdx2maz0fV61Xg81vF4VLfb\ntR3p47Cb4k9RFKmua0nS6XRSv9+3nMh9HLP+Pm3bajqdKssyjUYj23GcdTgcVBSFJCkIAvm+z0f7\nC1/x5wvz4jhW0zSaTCaSnmN+vJfnebYjOGu/3+t2u2m32ynPc3mep7Is1el0bEdzymAw0Gq1Upqm\nejweWq/XrPEL3GoEAIBhzAMAADCM8gUAwDDKFwAAwyhfAAAMo3wBADCM8gUAwDDKFwAAwyhfAAAM\n+wGxKljfpVKZ6AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11194e6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the dashed lines touch a couple of the points: these points are the pivotal pieces of this fit, and are known as the *support vectors* (giving the algorithm its name).\n",
    "In scikit-learn, these are stored in the ``support_vectors_`` attribute of the classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9jyYjsSERBZEXUD71Hqa8w17AQ6lU4sQXxyAo5cEQbMTAZ4cgKi7aDVET4j1otjNpVdNW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\niC8AAMaILwAAxogvAADGiC8AAMb+A9MpAt69PM0oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1119ab7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf)\n",
    "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
    "            s=200, facecolors='none');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use IPython's ``interact`` functionality to explore how the distribution of points affects the support vectors and the discriminative fit.\n",
    "(This is only available in IPython 2.0+, and will not work in a static view)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wPL/FYmHHjgvC8lxChMvs7AyaFjjzHR8fAwL9DlZrA4piw2ptOOOCJUJEwrqD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\nRQwAgEEUMQAABlHEAAAY9DtZs7XuFTVZkAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1119d09b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.html.widgets import interact\n",
    "\n",
    "def plot_svm(N=10):\n",
    "    X, y = make_blobs(n_samples=200, centers=2,\n",
    "                      random_state=0, cluster_std=0.60)\n",
    "    X = X[:N]\n",
    "    y = y[:N]\n",
    "    clf = SVC(kernel='linear')\n",
    "    clf.fit(X, y)\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "    plt.xlim(-1, 4)\n",
    "    plt.ylim(-1, 6)\n",
    "    plot_svc_decision_function(clf, plt.gca())\n",
    "    plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
    "                s=200, facecolors='none')\n",
    "    \n",
    "interact(plot_svm, N=[10, 200], kernel='linear');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the unique thing about SVM is that only the support vectors matter: that is, if you moved any of the other points without letting them cross the decision boundaries, they would have no effect on the classification results!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Going further: Kernel Methods\n",
    "\n",
    "Where SVM gets incredibly exciting is when it is used in conjunction with *kernels*.\n",
    "To motivate the need for kernels, let's look at some data which is not linearly separable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GjesEBAR6vefhw+mEh0dgNkcRGOj9HHF/NpuNAxv2U22tYuDUIdKOPkiCsxCi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\nSyWvvw6/+pX7+X37wvnzlyg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v13sMi0dGmtBqtSiKwqczV/H83ufc7n1De4O9rx5kxAuj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\nhBBCSJSh5EwIIYREGUrOhBBCSJT5/1cQsQ3TaUnmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111a7bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_circles\n",
    "X, y = make_circles(100, factor=.1, noise=.1)\n",
    "\n",
    "clf = SVC(kernel='linear').fit(X, y)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, no linear discrimination will ever separate these data.\n",
    "One way we can adjust this is to apply a **kernel**, which is some functional transformation of the input data.\n",
    "\n",
    "For example, one simple model we could use is a **radial basis function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r = np.exp(-(X[:, 0] ** 2 + X[:, 1] ** 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plot this along with our data, we can see the effect of it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lTSGt3UyKLxjBc2qs+IIsl6fHo2AW5qFDB/HQQ9/Ct771Pcvrr732Cn7yk4ch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\nPl8NvN5qiKIPgiDGCi4oigx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T+gN2ZVKRQT/BYBCjo1cxMjKM+vo60zu0BPQ4hzP5lIVn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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111df43c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "\n",
    "def plot_3D(elev=30, azim=30):\n",
    "    ax = plt.subplot(projection='3d')\n",
    "    ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap='spring')\n",
    "    ax.view_init(elev=elev, azim=azim)\n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_ylabel('y')\n",
    "    ax.set_zlabel('r')\n",
    "\n",
    "interact(plot_3D, elev=[-90, 90], azip=(-180, 180));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that with this additional dimension, the data becomes trivially linearly separable!\n",
    "This is a relatively simple kernel; SVM has a more sophisticated version of this kernel built-in to the process. This is accomplished by using ``kernel='rbf'``, short for *radial basis function*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IKGFhYfj5BUzoTmfW1tasWrUGd3d3zp07y5kzmezc+ZVh1SLY2dmx5KvLRyGV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111df9828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clf = SVC(kernel='rbf')\n",
    "clf.fit(X, y)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf)\n",
    "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
    "            s=200, facecolors='none');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here there are effectively $N$ basis functions: one centered at each point! Through a clever mathematical trick, this computation proceeds very efficiently using the \"Kernel Trick\", without actually constructing the matrix of kernel evaluations.\n",
    "\n",
    "We'll leave SVMs for the time being and take a look at another classification algorithm: Random Forests."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
